So I have been looking in to mobile power sources and potentially the answer is to make the case with lighter things
D Class amplifiers can be quite punchy and are normally far smaller/lighter than conventional car amps.
Then the other thing is something like lithium battery packs (like the phone chargers) and a boost buck converter.
Depends on your skills with electrical stuff really, but the only way to go lighter is with lithium batteries.
One possible thing to look at is the RC plan battieres, pretty sure they come in lithium and 12v.
Whats the rating of your current battery and how long does it last? I'm guessing its about 7ah 12v? I guess you could maybe use power tool batteries might be a bit lighter, but getting 12v ones could be more of an issue as they seem to be 10.8 and 18v these days.