Ok both of these are tpgk/tptk hands. One is played passively on the turn and one is not. My questions are what is the right way to play these?

Hand 1.

PokerStars No-Limit Hold'em, $1.00 BB (6 handed) from (Format: Bet The Pot)

SB ($97.25)
BB ($11.10)
Hero ($100)
MP ($468.65)
CO ($98.50)
Button ($59.50)

Preflop: Hero is UTG with , .
Hero calls $1, 2 folds, Button calls $1, 1 fold, BB checks.

Flop: ($3.50) , , (3 players)
BB checks, Hero bets $5, Button calls $5, BB folds.

Turn: ($13.50) (2 players)
Hero checks, Button bets $6, Hero calls $6.

River: ($25.50) (2 players)
Hero checks, Button bets $12, Hero calls $12.

Final Pot: $49.50

This one was played very passively with the check on the turn. It just seems really WT playing this passive....but can I really fold to these weak bets?

Hand 2

PokerStars No-Limit Hold'em, $1.00 BB (5 handed) from (Format: Bet The Pot)

MP ($41.40)
Button ($39.50)
Hero ($112.40)
BB ($37.35)
UTG ($99.35)

Preflop: Hero is SB with , .
UTG calls $1, 2 folds, Hero completes, BB checks.

Flop: ($3) , , (3 players)
Hero bets $3, BB calls $3, UTG folds.

Turn: ($9) (2 players)
Hero bets $6, BB calls $6.

River: ($21) (2 players)
Hero checks, BB bets $7, Hero calls $7.

Final Pot: $35

On this one I bet the turn...which I am not sure it's the right play or not but meh...I check behind on the rive, 1. b/c I don't really think my hand is all that good and 2. if he was on the flulsh draw I want to give him a chance to bluff at the pot. And I have to call the small river bet right?

You should really keep pounding until you have been given a reason not to (ie been raised)

Hand 1 I would have bet the turn 3/4 to full pot. He called the flop and while you hate to see middle pair potentially trip, it is extremely weak to check call the rest of the way as soon as that situation arises. If you throw out a strong bet and he raises you can muck. If he calls you can check-call or otherwise re-evaluate on the river.

Had 2 you played better. I would have put a little more into the pot on the turn but otherwise its fine. The board is dangerous so your check-call is a good way to get to showdown here.