Some gens like my little Honda 1kW have a mode that throttles way back if the load is low to conserve. Lot less noisy too. Not that I would buy another one soon, but this one can be hooked in parallel with another for 2kW is you had to have that.
I've got one of those and really like it. I use 100 LL aviation fuel for my small engines that are going to be sitting for awhile. My pressure cleaner sat for over 2 years and started with just a few pulls.
“but this one can be hooked in parallel with another for 2kW is you had to have that. “
Do not do that - if they get out of phase, you will fry everything.
My company actually tried to invent a device to allow that behavior - two multi-million-dollar labs went down in flames.
YMMV.