With top pair out of position on low-connected runouts, favor checking and small sizing to keep Villain's range wide.
Checking or betting small is the standard approach here. When betting, sizing down to around 20% of the pot accomplishes the same protection and value without isolating against stronger holdings.
Note: Betting 66% pot OOP bloats the pot unnecessarily; prefer checking or using a small ~20% pot sizing.
Checking is preferred on this turn card. The four brings completed wheel straights and hits CO's calling range hard, making a second barrel relatively thin.
Note: Barreling on a wheel-completing turn runs into CO's improved range; checking to realize equity and control the pot is higher EV.
Checking is mandatory. The board completes a five-card wheel straight, meaning we cannot bet for value unless we hold a six.
Calling is standard here. We are playing the board straight, meaning we chop against almost all of CO's range and only lose to holdings containing a six like pocket sixes.