you could implement an enemy like the thiefs in slay the spire. They were a fleeing type enemy that would steel 45 of your gold at the start of combat(or 15 each hit, I forget). If you can’t kill them fast enough you loose your gold.
You could do something similar. perhaps the first attack the enemy makes steals some weight then they plan on running. Or have them steal weight when they start the fight then flee like a normal fleeing type.
A fun Idea for a boss that gains weight is a boss that eats their allies. It could create a sort of race to see who can eat the most. I see 2 ways to make it a challenge for the players. you can gain more weight if you eat bad guys faster than the boss, or the boss takes their time and burns your clock if you want to see the weight gain.