Honda 2000 and AC and Microwave problems

We have a very small microwave, and our Honda 2000 will power it, but it is not pretty -- the lights dim, the microwave struggles, and the generator races. We use the microwave about three times a year, at most -- DW loves microwave popcorn, so it is a rare and special treat.

I would not even try to run my A/C with our generator -- I don't want to hurt either one of them!