It wasn't clear to me from your post if you're either playing sitting down or standing, but I'm guessing since you emphasized the weight, you're standing. Yet personally I always get aches from playing sitting down, as I forget about my posture and slump, which feels fine at the time, but it hurts the next day. I guess there's a few things that I might try though...
*get a comfortable strap
*take a break (at least once an hour or more if you're not already)
*save $ for your own new guitar, but meanwhile...
*try to improve the performance of your crappy guitar (set-up, pickups, other hardware)

And no, you shouldn't just put up with it, as it could lead to chronic pain...not fun, and potentially debilitating.