Typical situation that gives me trouble.
Raise in EP with 1010-QQ, get 1 caller pre and flop comes semi-dry with a non ace over card. V is usually weak passive player.

Recent hand as example:
Her0 UTG ($500): 1010, mid 30's, taggish image.
V HJ ($200): 40's weak passive. Hasn't raised preflop in 2 hours he has been there, has shown down AK, AJ and similar at showdown failing to raise limpers and open limping with them.

Hero raise UTG with 1010 to $10 preflop.
Folds to V who calls in the HJ, all others fold.

Flop ($23): Q 9 2 r
Hero bets $15, V calls.

Turn ($53): Q 9 2 4 r
Hero?

I give a typical weak passive a flop range of Qx, 9x, J10, gutshots, sets, any pocket pair(less likely AA/KK/1010) and AK, and a tiny portion of Ax. I think most everything else folds, these guys aren't floating etc...

I feel like a turn bet of say $35 or so only gets called when we are beat with the exception of J10. These guys usually can call wide on the flop but tighten up to bigger turn bets. While these guys are weak passive, some will bet the turn a little wider with lots of pairs if I check the turn, cause "i must have AK and been just c-betting the flop and don't want to give me a free A/K to beat their pair".

I don't think I ever get 3 streets of value, if the hand goes b/b/b, villain almost never shows up with a worse hand on the river.

Turn/River Plan?

Cbet then x/f or x/c (mostly x/f).

It's also ok to NOT c-bet.

They will always put you on AK anyway.

Against weak passive players on a dry flop with an over to your pair you are probably only getting called by a better hand most of the time. ie, your bet probably won't work as a bluff OR a value bet.

You may get value from a blank turn bet having checked the flop. You also keep the pot small hating a lot of turns that passive villains will never bluff at.

At the end of the day, you still have a pretty weak hand. One pair with very little chance of improving.

cbetting here 95% of the time and then mostly x/f and possibly x/c OTR if the turn is checked through and the river blanks. While I think it's possible V show up here with A9/KJ/T9 sometimes I'd rather play against these guys when we have position.

I bet 15 on the turn. Value from 55-88, 9x and an easy fold if raised given he's passive. Passive guys might even check back aq on the river after you've raised and bet twice.

OOP, I check-call this twice and bet the next street any time V allows this to go check-check. I fold to a third barrel on run outs against most villains. If the villain is very straight forward, I might fold the second barrel.

Betting flop and checking turn opens me up too an auto bluff from most villains.

I like this line. It feels like you're lighting money on fire if you c-bet the flop and c/f the turn. Most Vs do know what a C-bet is and they know you don't necessarily need a hand to bet the flop. A turn check after a c-bet wreaks of weakness.

Grunch:

Board and villain dependent imo. If there are draws out there and you have a villain with a loose preflop calling range, I'd barrel two streets if draws miss and check back river.

Versus a tighter villain on a dry board I am checking flop and re-evaluating. If it's a total nit I can c/f flop, if it's someone aggressive who could make a move, I'm c/c reasonable bet sizes on two streets. If flop checks through, I'm betting 1/2 pot on most turns and rivers.

I don't think there is one correct answer to this, but I will say that on a dry board we can often get two streets of value from worse by checking flop, where we will get mostly folds or called by a Q if we bet flop.