Is it normal to have my period for more than 2 weeks while on birth control?

Depends: Breakthrough bleeding is very common on birth control pills and generally lasts only one cycle. Other causes of irregular bleeding on the pill include infection, pregnancy, polyps, etc.

Yes: Breakthrough bleeding on birth control is common. If it persists, or occurs more than twicw a year, get checked for a possible change.

Breakthrough bleed: Unscheduled bleeding is a common side effect of any birth control method but very common on low dose pills. It usually corrects itself in a few days or over a couple of cycles. If not then you will need to schedule a visit to discuss changing brands or changing methods and make sure nothing else is wrong. Other than being annoying for you it is not harmful.