How does the key size per data bit influence the security?
Quite apart from the correction that Reid made (it takes $2^{127}$ attempts to achieve a probability of 50% of finding the right key; with $2^{64}$ attempts, the probability of success is $2^{-64}$), with AES, there is no known way to take advantage of known (or even chosen) plaintext to speed up any brute force search; even with $2^{64}$ chosen plaintext/ciphertext pairs, the best known attack is to pick one pair, and apply a brute force search on that pair.