If a villain called my 3X turn raise, generally, should I size my river value bet 2/3 pot as opposed to 1/2 pot because he's shown so much strength?

Very "it depends" question, but if you have the near nuts and made a big raise OTT, I'd get as much as possible into the river, up to and including an overbet shove. Def would never bet only half pot unless we have a read he was just overpaying for a draw and it bricked, but might have caught a pair.

Way too open ended on this one ... it depends.

Did you c/r Turn? (position please)
Did the board get 'better' or blank?
Did your hand improve?
How deep are you both?
Nit or station for opponent ... and your image?
Do you want a call?

Generally speaking if you go from a large raise to a 'value' sized bet you are going to get called. Any bet near 50% of the pot looks fairly weak and may get raised as well. In order to avoid a tough decision I like to block bet 60% pot ... but decide if you are folding to a raise before you put it out there. GL

I'd love a call for as much as possible, my hand is very strong, and I'd love to get it in. 100bb eff.

P.S. What do you mean by "Did the board get 'better' or blank?"

Did the River card improve any draws or was it the 'old' 2s?

Generally speaking you can bet a bit bigger on the River against some opponents if a blank hits since it can look more like a bluff than a value bet ... an extra 15%+ of a 'normal' bet. The bet size can be ignored due to the fact that neither hand improved on the River in the opponents eyes and they were either going to call he River (with made hand) or not (missed draw).

If the completed board has the potential to improve 'a hand' then it comes down to images. If your opponent thinks you were on a draw then you may need to bet smaller to get the 'crying call'. If you still think your hand is good and the River card helped your opponent then a bigger bet is better to extract full value.

One would assume that if your opponent called such a large raise that they already had a made hand, put you on air or had a huge draw and the River card will determine what bet size is best for the situation. GL