Alphabetic Substitution with Symbols
If I understand your cipher idea right, you would have a larger ciphertext alphabet than the plaintext alphabet, where each plaintext symbol maps to multiple ciphertext symbols (and the number is dependent on the frequency of the plaintext symbol), one of which is used randomly.

This is known as a Homophonic substitution, and with it the single-symbol frequency analysis usable for simple substitution ciphers is thwarted, since all symbols now have similar frequencies.

But as soon as we start to look at frequencies of letter-pairs (and triplets), we will observe enough structures to break this, too. For example, q is almost always followed by u, and thus the ciphertexts of q will almost always be followed by one of the ciphertexts of u. (I don't know enough about the statistic properties of the English language to give more examples, but you can be sure that an attacker would know.)

Some examples from German:


As in English, q is almost always followed by u.
A c is almost always followed by either k or h.
ei has about same frequency as ie (and i is the only letter who has this property related to e).


Some more details are given in David's answer.

Of course, if the ciphertext is so short (or the translation table so large) that each symbol is only used once or twice (or not at all), cryptanalysis is more difficult (or even impossible).