ie. an EV that needs to produce 1kW might use 1.1kW from the battery and when it needs to produce 2kW it might draw 2.2kW (~2x) from the battery. So 10% increase in weight might result in a 10% reduction in range.
An ICE that needs 1kW mechanical energy will probably burn 10kW worth of petrol; when it needs 2kW of mechanical energy it’ll burn 11kW (<2x) of petrol. So a 10% increase in weight would result in a <10% reduction in range.
Directionally, your numbers are right, but we'd be looking at more like 5 kW to idle an ICE regardless, and then 6 kW for 1 kW output and 7kW for 2kW output (efficiency going from 17% to 29%). Instead of doubling output though, we'd only need to go from 1 kW to ~1.035 kW if we increased mass by 10%.
Which brings us to the topic of the batteries being heavy AF, but that's a whole other question.