Does Grover's algorithm effect block size or only key size?
It depends on the application. If you are using the block cipher as a hash function or for a MAC (say in CBC-MAC fashion), then it very well could create problems. Preimage attacks would be much easier than they should.

For normal encryption, however, there wouldn't be a problem since the key is not known to the attacker. As evidence of this, consider Triple DES which has a 64 bit block size yet is still sufficiently secure for use today (though I wouldn't recommend it in newer designs).