Re: Maybe there is nothing to think about here....?
When you raise preflop you are representing a range of possible holdings. There are very few that contain a 2. When V CC's your preflop raise he is also representing a range. This is better defined by you as you may know his tendencies.
When he raises your bet OTF he is representing a significantly smaller range. That being (super standard) overpairs and (more advanced) a flush draw wishing for a free card. He could also have just over cards, but I think to make this raise (with overs) he likely would have 3! preflop. As he CC'd preflop we can somewhat narrow his ability down to sub standard (if unknown). Basically this means his chance of having overs is diminished imo.
By just calling OTF we leave our range somewhat open. This is for deception. However, he has declared that he likes his hand. This means he is likely to call a raise and possibly call down. (unless you have a strong read that villian will fold to a flop 3! then you should usually cap and lead w/ a strong hand (paraphrased WithG) *just giving credit where it's due. Thought it was my thought then realized it wasn't)
So if we 3! his flop raise then our range shrinks up a bit. Mostly to 77+ or somelike. This also has deception because he still thinks he's got a chance to outdraw your range.
If he has overs then he calls this and maybe a turn bet (and river if improves).
If he has an overpair then he calls down or gets aggro OTF then calls down.
If he has a draw and misses he calls turn bet and calls or raises improved rivers. If he improves on the turn then you capture 3 bets OTT +1 OTR.
However, if you just call the flop and go for a check raise on the turn then you get free carded very often (zero bets). You check raise a made draw (2 bets). You check raise an over pair (2 bets). You check raise an idiot that is overly aggro with draws OTT (2 bets). This is as far as I'm going with the verbose version of 'yes, cap and lead'.
In these small games (often higher as well) a turn raise tends to represent huge strength. A turn check raise is even more so. Most players seem to think the turn raise with 2 pair + to be the pinnacle of thinking in limit. Thus they assume you think this as well. They further think that it's a bad idea to raise a turn with less than board rank best (meaning if a flush is possible you must have that, str8, house, etc). Thus when you raise a turn with these guys they are likely to shut down.