Now we're in what's essentially a side-pot and I certainly don't think I can make a PSB, so the question is how much to bet if we decide to re-open the action. 

While it's slim that the MP would be motivated to raise the flop his AXss hands, it's hard to think of what else check-calls (or check-raises) this river after raising the flop and checking the turn on a pretty dangerous board when my range on the turn is so combo-draw heavy.  

The fact that it's a side-pot cancels out arguments for betting here to balance bluffs, and so we need to be pure value.  Our range is pretty protected against a raise, but at the same time, Villain has no reason to continue with anything other than the nuts on this board, given how the action played out. 

Is a check here that ridiculous?