Is it more weak to encrypt with the private key RSA? I have a simple question.

Is it more weak to encrypt with the private key against the public key with RSA ?

Like is it easier to "crack", "brake", "solve", "decrypt" when I encrypt with the private key against the public key. Is it really the same process of encryption?

(In both cases we assume that the "breaker" doesn't know any of the keys)

Edit:

To be more precise, is there something that differs in the process of encryption with any of these two keys.

Is the only difference between the public and private is that the private can generate public keys but the public key can not generate private? If I want to encrypt with the private or the public key the result is the same, the encryption is passing by the same steps and then results in a difficult breakable encrypted output?


RSA key generated with puttygen
PGP encryption / decryption
the "breaker" doesn't know any of the keys


That goes against the very name of the public key, and rationale for using RSA or any asymmetric cryptography. Let's assume it nevertheless in the first section of this answer.


  Is the only difference between the public and private (keys) that the private can generate public keys but the public key can not generate private?


No.


The two keys typically are not in the same format.
Further, in RSA


The exponent in the public key is customarily small.
The most common formats for private key include the factorization of the modulus, when the public key never does.
Depending on format of the private key and method of generation of the key pair, the private key allows to generate a matching public key, or not. Neither constitute a weakness of RSA.

The public key of any secure asymmetric cryptosystem never allows to generate a matching private key.



  (assume):
  
  
  RSA key generated with puttygen
  PGP encryption / decryption
  


PGP does not give any way to encrypt with a private key, nor decrypt with a public key. Neither does GPG, nor any reasonable OpenPGP implementation. The closest it allows is producing a signature, which leaves the message in clear or removes it. That's totally unsafe or dysfunctional from the perspective of confidential transmission of a message.
Note: When creating or importing a private key, PGP/GPG also generates or import the public key, and that what it uses to encrypt. Correspondingly, the passphrase normally required for private key use is not asked for encryption.

The closest feasible thing matching the question's description would be to swap the public and private key generated by puttygen, before somewhat feeding them to the encryption program. That's not quite trivial, because the two keys are not in the same format. But that's feasible: we change $e$ of the formerly public key to $d$ from the formerly private key, and change $d$, $d_p$ and $d_q$ of the formerly private key to the former $e$, that is $37$ as explained here.

If we do this, the newly made public key will look about normal, except for a large exponent instead of a customary short one ($37$ and $65537$ are common). Encryption will be possible (and measurably slower than usual). Decryption with the newly made private key will be possible (and measurably faster than usual). The question asks if that's less safe than normal encryption is.

Yes, that's less safe in the sense that now an adversary knows the normally secret $d$ in the private key (that's $37$). Thus if somewhat the normally public modulus $N$ gets public, it becomes trivial to decipher. Normally $N$ is in both keys, thus public; and further, encryption programs make no effort to keep $N$ secret: we can't rule out that with some encryption option, $N$ is sent in clear along the plaintext. Or that some attack allows the attacker to know $N$. For a start, PGP and GPG store $N$ in clear in the pubring file, not protected by a passphrase.

If we hypothesize that an attacker only has one ciphertext without $N$, I see no way to obtain $N$ or otherwise decipher or get any useful information about the plaintext.

This perhaps remains true if the attacker has multiple ciphertexts and knows some corresponding plaintexts, assuming hybrid encryption is used (as in OpenPGP). However, with textbook RSA encryption, $N$ can be recovered and security is lost.



[From this point onwards, we again assume the public key is public]


  Is it more weak to encrypt with the private key against the public key with RSA ?


Often that's impractical or/and unsafe (see above); but not necessarily. In fact, RSA as taught and practiced today reverses the public and private key compared to the key generation procedure of original RSA (Ronald L. Rivest, Adi Shamir, and Leonard  Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, in Communications of the ACM, Feb. 1978). That reversal was originally made for performance reasons, and it turns out that it improves security compared to that in original RSA!

Original RSA has an almost unique characteristic among asymmetric cryptosystems: we indeed can exchange public and private key, and that does not compromise security (including when we reveal the key used for encryption, as designed, see final section). That's because original RSA


first selects the decryption exponent $d$ mostly randomly in a large set, then computes the encryption exponent $e$ from that, per the symmetric equation $e\,d\equiv1\pmod{\phi(N)}$
public and private keys are in the same format: the public modulus $N$ and an exponent.


It quickly became standard practice to first choose the encryption exponent $e$ (that is, reverse public and private key compared to key generation of original RSA): in Martin Gardner's A new kind of cipher that would take millions of years to break (in the Mathematical Games column of Scientific American, Aug. 1977), Rivest's MIT group used $e=9007$ in a then difficult challenge, implying that $e$ was chosen before $d$. Such small $e$ speeds computations involving that exponent (encryption and signature verification) by a large factor, broadening the practical uses of RSA; but it becomes unsafe to exchange public and private exponents.

It took some time to fully realize that original RSA's prescription "It is important that $d$ should be chosen from a large enough set so that a cryptanalyst cannot find it by direct search" is necessary, but insufficient for security. Selecting a random $d$ in $[2^{135},2^{136}]$ with $\gcd(d,p-1)=1=\gcd(d,q-1)$ blocks direct search of $d$, but would be unsafe for $p$ and $q$ 512-bit or larger primes (see Dan Boneh and Glenn Durfee, Cryptanalysis of RSA with Private Key $d$ Less than $N^{0.292}$, in proceedings of Eurocrypt 1999).

In original RSA, decrypting is the same as signing, and both are encrypting with public key replaced by private key. However:


Original RSA's enciphering is insecure (among reasons: correct guess of the message can be verified with the public key, thus it is insecure to encipher a name on the class roll, a password, or a credit card number).
Original RSA's signing is insecure (for different reasons, including: an adversary can find signature of a message showing as any short desired text when printed as a C string; a few rightful signatures of some selected meaningful and sizable messages can be turned into forged signatures of other meaningful and sizable messages).


Weaknesses of original RSA have been fixed, but with modern RSA as practiced (or PGP/GPG and RSA keys), signing is markedly different from encrypting with public key replaced by private key. And many other common signature schemes have no encryption counterpart.

While modern RSA practice distinguish signing from encrypting with public key replaced by private key, it's possible to have the two use essentially the same padding. See Jean-Sébastien Coron, Marc Joye, David Naccache, Pascal Paillier, Universal Padding Schemes for RSA, in proceedings of Crypto 2002 (also there). Note: AFAIK it is not used in practice.



Glossary of things properly named:


In public-key cryptography, the public key is made public (the private key is kept secret).
In public-key encryption, encryption is with the public key (decryption is with the private key).
In public-key signature, signature verification is with the public key (signing was with the private key).