Do oral contraceptives affect a woman's metabolism?

No negative effect on metabolism has been found.[1][2]

Other studies found that women on oral contraceptives had slightly (3-5%) raised metabolism.[3][4]

We can safely concluded that there is no negative effect on your metabolism from oral contraceptives, and it may actually increase it slightly.

Oral contraceptives based on antiandrogens may make it harder to gain muscle mass,[5] but there is still far too little research in that area to make a statement of certainty.