What would be the lightest batteries to run a 12v/12.5A skillet for 2 hours?
A butane-propane canister contains 12000 Wh per kg of gas.

A Li-Ion battery contains about 100-200 Wh per kg.

As you can see, energy density is merciless. I'm tempted to say "end of story" here, although you should also consider cost, which leans heavily on the gas burner's side.

Also if you want to cook a steak, you need a 2kW burner, which is readily available... bit more complicated on battery power...