Overload light eu3000 comes on with trailer roof ac never did before

The battery is really only there for the electric start. Put a digital volt meter on it while running it under the load of the AC unit. Or if it goes off on the overload with the AC unit, try a variable load like an electric heater or two that you can switch on in steps. Most space heaters or hair dryers have a 1000w, 1250w 1500w so you can increase the load. Watch what the voltage does. If at 1500-2500 watt load the voltage starts to drop drastically, say from 125v down to 90 or 80v as the load increases, that usually indicates a problem with it not getting enough fuel. On these inverter generators, the carburetor is controlled by the inverter by the use of a throttle motor. As the inverter senses the demand for more power, it increases the throttle to deliver more horse power of the engine, thus meeting the demand for more electrical power out.
I have seen a couple things cause this. A partially plugged jet in the carburetor can cause it. A bad throttle motor (Part# 21) on the top of the carb can go bad. I even had one that I caused myself by not putting the little spring (part #20 on the exploded view of the carb) that sits under the throttle motor in correctly.