At the lower level, my general approach (which proved very successful and I think still holds true) is to play your stronger hands pretty aggressively, as you did in both of these hands.

Hand 1:

PF, your 3bet is a little larger than standard, but if he's going to call a big 3bet with hands such as A4s or even weaker, then there is nothing at all wrong with your 3-bet size, it's actually very good.  Postflop is completely standard, there's no way you don't get it in with a smile on your face if you have an overpair vs a lag in a lower buyin game (hell, any buyin level you're not folding on that flop against anybody).

I would probably not bet so large on the flop, you want to encourage the lag to raise your flop bet as much as possible.  That doesn't mean you get fancy and bet 200 or check, but a 300-400 chip bet looks like it has a lot more fold equity to your opponent than a 600 chip bet.  And if he calls the 400 chip bet with a draw, he can only gain around 800 more total chips, so it's not like you're "pricing him in" to make a loose flop call, it's his loss in the long run if he calls light draws in that spot on that flop.  You can now see how your big preflop 3bet and his loose call basically allows him no room for manuevering postflop if you play at all competently (by betting reasonable amounts such as half pot or bigger).

Hand 2:

He's loose, he's aggressive, the board has a lot of action on it and you have TP, 3rd kicker with a gutshot.  You are well ahead of your opponent's hand range that will likely play a massive pot on this flop, so your check raise is fine and you're too strong to think about folding to his shove.

You don't need such a large flop raise, but again, like hand one, if he's going to be calling or reraising quite a bit, there's not going to be many spots where you should or could bluff, so a bigger raise (or bet size) can be appropriate on earlier streets (or preflop) where this guy will do nothing but call your aggressive plays.  This also means you're only betting or raising big for value most of the time, so a big size works well within that counter strategy.

It'll get a little trickier as you move up and the lags actually learn to fold in spots, but you can deal with that as you move up.  For now, you look to be playing a very solid early street value aggression type strategy against these lags.  Keep it up.

No problem.