There is very little research on the biomechanics of various heel drop heights in running shoes (believe me, I've looked...). So far it appears that heel heights have a moderate effect on how you hit the ground. Generally speaking, higher heel = slightly more force going into the heel, shin, and knee. Lower heel = slightly more force in ankle, Achilles, and calf.
Whether or not more heel drop alters hip mechanics is an open question. That's going awfully far up the kinetic chain from the ground, so it's hard to say with much certainty what's going to happen. But shoes do not appear to have much influence on injury risk overall, so I doubt that any particular shoe type causes weak hips.
Runners as a whole tend to have weak hips, and this is associated with a number of injuries. As to why runners have weak hips, that is also unknown. Nobody's really sure why. In my personal opinion, the two leading hypotheses are:
1) runners move almost entirely in the sagittal plane (i.e. forward/backward) and are underdeveloped in the frontal and transverse plane
2) A relatively sedentary lifestyle with a lot of sitting creates hip muscle weakness and dysfunction
There is exactly zero evidence for either of these ideas, however (as of right now, at least).