Struggling with generator size

My Yamaha2400 will run the AC,(13,500), but, everything else has to be off, sometimes, including unplugging the converter. That means the refer has to be on propane and the electric element in the HWH off. I understand there are some, older AC's with higher starting loads that the 2400 will not run. I find, in the mountains, I seldom need the AC. I do have 100 watts of solar which helps a lot. I only need to run the generator every three or four days for battery charging. Thinking about going to LED lights. I think the solar would almost keep up with charging then. I went with the 2400 because I wanted something that would run the AC if necessary but that I can lift. I have a frame mounted hitch on the back of the TT and carry the generator on a rack on that. The 2400 is about 80lbs with fuel. A 3000 at 150lbs is more than this old man wants to,(can), lift. The Yamaha is very quiet. It more than covers the bases for battery charging, running the micro wave, hair drier etc.