Do hobby scale welders draw less amps doing lighter jobs?

Buying a hobby grade stick welder was probably a poor choice, a MIG being much more flexible and easier to use. But since you have it, the problem with current draw is that the welder is going to peak when the stick starts the arc and when the rod gets stuck and pulled free and it may be using under 15 amps at the time, but might peak out at 22-24 amps briefly which a 20 amp breaker may allow but is too much for 15 amp. Perhaps more importantly, if you have a 15 amp breaker, you should have 14 gauge, not 12 gauge, wire attached to it, and running at close to 15 amps for any length of time may heat the wires, as 80% usage is considered a good limit.