How best to deal with min-bets on flop/turn?

shakinaces

I can't help but think this is one of my major leaks at the moment, dripping money away unnecessarily.

With increasingly regularlity I find that, after raising pre-flop in position (between 2.5x - 4x) and getting called by one or both of the blinds, I then face a min-donk-bet (potentially as little as 1bb into a 12bb pot).

Whichever route I take from there (call or raise) I face another min-bet on the turn before a shove/overbet on the river.

I struggle to fold to these tiny bets, it just seems so weak when I'm sat there with a hand that was worthy of an initial raise (pocket pair, big ace etc).  Yet when not hitting the flop in any meaningful way, it's hard to get carried away knowing that I'm going to face a shove on the river that I can't really call with ace-high/3rd pair or lower if I (as is the norm) haven't improved.

Should I just be cutting my losses and taking the decision to fold to the initial donk-bet, unless flopping big/big draw? 

I figure that calling flop and turn to hit a set would be offering the implied odds to make it an ok play, but just feels that its so rare to hit the two-outer (which may not even then be the best hand) it's still going to be a losing play.

WHOAMI196

treat min donk bets as a 'check', sometimes it can indicate strength in some players but mostly it is bottom/weak pair, draws or air. 

so you have AK you open UTG, get called by the a fish in BB, board comes 8,9,j and fish min-donks!? What do we do??? well its likely he has a piece of it and will unlikely fold to a raise if he does, so calling is fine, you have two overs and possible back door draws, but on this board folding is also fine because even if you hit an A or K you likely only going to get a little value when you get to showdown.

Same scenario but board comes 5x5d6d, in this spot imo best to 'raise' or c-bet when it comes to my philosophy, on this board you are likely to have the best hand and the villain could have draws, weak two overs etc, so raising will likely win you the pot, even if he calls.