Microwave keeps tripping breaker
I live in a house that's about 35 years old, and it has a (probably) brand new over the range microwave. I know that the microwave, the overhead light, the refrigerator, and the stove are all on this same circuit. What I'm experiencing is that, if I run the microwave for very long, it trips the circuit. I've noticed that if I only run it for 30 second intervals, it usually doesn't trip it, but occasionally does. It does this regardless of whether I have the light or anything else on (obviously the refrigerator is always on).
Is it likely that the breaker just needs to be replaced or is it likely that it needs to either be upgraded to a 20amp circuit or have a new circuit installed for the microwave? I also have another breaker that tripped just from a light burning out, so I wasn't sure if it's possible that the problem is just that the breakers are old.
Thanks for any suggestions.