"Just have to be bigger"?

I want lighter guitar amps that don't cost an arm and a leg, dammit! :)

Then go solid-state.

Inverter-based power supplies are sufficiently light that a guitar amp should only be the weight of the wood and the speakers.

And, the speakers have to be a certain size to move the correct amount of air--so the copper coil is probably the limiting weight. It's remarkable how much air you have to actually move to get decent sound volume.

Hm...sounds plausible from a physics POV, but maybe there's something else? Since, in practice (at least as far as I can speak from experience), old-school ferrit 15" speakers are ~7-8kgs, while you can get similarly specced neodymium speakers that weigh about half (3-4kgs).

Maybe ferrite, but you can also get ceramic magnets:

Ceramic 4.4lbs 50W http://celestion.com/product/20/rocket_50/

Neodymium 3.7lbs 60W http://celestion.com/product/14/g12_century_vintage/

And, yes, you will find that the values are all over the map in terms of weight. There are some much less powerful speakers that are quite a bit heavier.