How does changing input size affect The Goldreich-Goldwasser-Micali Construction?
The input size and the key size need not have any specific relation. The security analysis of GGM goes through as long as the key size is equal to the seed size of a secure length-doubling pseudorandom generator, independently of the input size, which can be an arbitrary polynomial in the security parameter.

Since the depth of the GGM tree is exactly the input length, if you double the input length, you indeed double the depth of the tree. The security analysis remains identical: the only difference is the number of hybrids in the proof, but changing the number of hybrids by any polynomial amount does not harm security, since the adversary has negligible advantage in distinguishing any two hybrids.