My 15 amp circuit breaker for 2 bedrooms trips whenever either of the overhead lights are turned on but also if more than a couple of low amperage things are used in any of the receptacles (radio, low voltage light). I assumed the circuit breaker was the problem so I traded circuit breaker locations. The new circuit breaker had the same problem. The home is about 1 year old, it was professionally wired and it is not a GFI circuit.
The only real solution here is to actually measure the amount of current being drawn by the circuit.
This could be done by any number of jury-rigged methods using a multi-meter. But the safest, most effective would be to use a "clamp-amp" or "amprobe" style meter:
If the meter shows a load around the rating of the breaker (15 A), then you need to remove some of the loads on the circuit, and or have the rooms split into two circuits.
If the meter shows a load far below 15 A, then it's likely that the breaker is faulty and needs to be replaced.