CO vs. BTN battles/RR-ed pots/PF stuff

[orange]

Okay, that thread that shpanko had a bit ago had me thinking a little bit about some situations. This is more geared toward CO vs. BTN battles or BTN vs. blind (in which hand ranges are a bit wider than normal) and reraised pots.

In this thread, carrot alluded by saying he'd rather 3-bet 32o than 22 or 33. I agree with this, it takes away from the value of the hand, etc. This thread also reminded me of a thread a long time ago in which me and BalugaWhale were arguing about the merits of reraising a CO opener with 77 when on the button. (can't find the thread doh).

BUT, in reraised pots, we (generally) are not going to be going to showdown with 32o (without a very good hand, ie. a straight or 22x flop or something of that sort). We are more reraising the hand for the value of position and the hope that we will GENERALLY take it down on the flop.

ie:
CO opens, we RR with 32o, he calls. Flop comes xxx and he checks and folds.

We of course are not raising for the pure value of our hand (as in AA) nor are we really raising for deception (well, in a way I suppose, in the sense that we need a pretty large hand in the way that 67s would need to continue in a rr pot). Moreso the value of this position and steal equity on the flop.

So, where is the Question?

22 and 32o both improve rarely. And both are crushers when we DO decide to felt in rr-ed pots. However, CAN 22 be used for this steal value? ie. CO opens, you have 22 on the button and...?

I never reraise here. But thinking about 32o and how often it improves (rarely) and how often 22 improves (rarely), can we profitablly reraise 22 here?

Unlike 77 or 99 and other low-medium pps, 22 doesn't have great showdown value. Take situation 1)

all fold to taggy CO, he opens, we have 22 otb and call, blinds fold. flop comes xxx, he bets, we raise, he folds.

2) all fold to taggy CO, he opens, we have 22 otb and RR, he calls, blinds fold. flop comes xxx, he checks and folds to our 2/3rds.

Now, what is the difference of play here? some observations:
-by reraising, we negate our positional advantage by expanding the pot size and therefore leaving us with little room to maneuver.
-by reraising, we potentially win a pot that we may not have won had we just cold called (ie. flop comes somewhat nasty, we aren't capable of raising/etc). unlike 77 or 88 or whatever, 22 does NOT have great showdown value (albiet some) and we generally cannot just raise for either value (in which some maniacs/lags will call with worse pairs/etc).
-yes, we won the pot in both situations, just got there differently.

And this somewhat applies to BTN or CO vs. Blinds battles. Again, we often reraise PPs from the bb for many reasons stated. We win the pot in a situation where we may not have otherwise (ie. btn opens, you cold call with 22 in the bb, flop comes xxx and you c/f. alternately, btn opens, you rr with 22, he calls and you bet xxx board and he folds).

so, what am i really asking?

not really sure yet. this is a long rambled post based off of positional battles (mainly LP battles) and the mixing of hand ranges and minimal showdown values.

Basically, if reraising a CO opener with 32o on the button is +EV (it has to be in general, given unknown, no reads/history,etc, right?), then why not 22? or 44?

hope that carrot will come in and butcher my thoughts.