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.

References

1.^Roy S, Mishell DR Jr, Gray G, Dozono-Takano R, Brenner PF, Eide I, de Quattro V, Shaw STComparison of metabolic and clinical effects of four oral contraceptive formulations and a contraceptive vaginal ringAm J Obstet Gynecol.(1980 Apr 1)
3.^Diffey B, Piers LS, Soares MJ, O'Dea KThe effect of oral contraceptive agents on the basal metabolic rate of young womenBr J Nutr.(1997 Jun)
4.^Piers LS, Diffey B, Soares MJ, Frandsen SL, McCormack LM, Lutschini MJ, O'Dea KThe validity of predicting the basal metabolic rate of young Australian men and womenEur J Clin Nutr.(1997 May)