What are the security effects of reusing a public RSA key to encrypt large data by blocks? I'm trying to figure out a way to do public key encryption on a very large piece of data.

For this, I of course want one side to do the encrypting but is unable to decrypt the data, and the other side to be able to decrypt data.

But for RSA encryption, there's a limit to the reasonable size-performance on how big it can encrypt. 

I haven't really figured out a good solution to this problem, but the simplest one that comes to mind is to just reuse the public key to encrypt the data in blocks. Of course, this would create some sort of security problems, but as of right now I still don't exactly know what kind of security problems it would cause. 

Could someone explain to me what problems this simple method would cause and perhaps also tell me of a way to achieve my goal of being able to do public key encryption on a large piece of data?
I assume that by 


  I want one side to do the encrypting but is unable to decrypt the data


you meant a general "encrypting only" party, since if you are talking about a specific piece of data, it does not make sense to disallow the encrypting party from decrypting that data since that party had the data already in the clear. 

If that is the case, then your goal might be achieved by first encrypting the data with a symmetric algorithm like AES, which can do big data rather efficiently, and then encrypt the symmetric key/PW with the RSA algorithm. That way, only the other party, who has the private key for the RSA algorithm, can decrypt the RSA-protected symmetric key and then proceed to decrypt the big data.