Bigger Bet on Turn?

Hi all, I just started playing online not long ago, and I'm always looking for help. I was wondering if you could give me some advice:

My opponent is loose-weak, and I've noticed him calling with garbage hands from the small blind before, especially in an unraised pot.

PokerStars Game #2866870500: Hold'em No Limit ($0.05/$0.10) - 2005/10/22 - 17:28:32 (ET)
Table 'Phobos' Seat #8 is the button
Seat 1: dwfarrel ($13.65 in chips)
Seat 2: OllieFitz ($2.70 in chips)
Seat 3: hottoddy ($10 in chips)
Seat 4: mr5375 ($3.95 in chips)
Seat 5: Mastamune ($9.85 in chips)
Seat 6: kamagong ($5.45 in chips)
Seat 7: Retardo99 ($1.85 in chips)
Seat 8: s8oy321 ($17.80 in chips)
Seat 9: Millr_HiLife ($11.90 in chips)

Millr_HiLife: posts small blind $0.05
dwfarrel: posts big blind $0.10
hottoddy: posts big blind $0.10

*** HOLE CARDS ***
Dealt to dwfarrel [Jd 4h]
OllieFitz: folds
hottoddy: checks
mr5375: folds
Mastamune: folds
kamagong: folds
Retardo99: folds
s8oy321: folds
Millr_HiLife: calls $0.05
dwfarrel: checks

*** FLOP *** [Js 6s 5c]
Millr_HiLife: checks
dwfarrel: bets $0.60
hottoddy: folds
Millr_HiLife: calls $0.60

I bet out here, firstly for information, secondly to try to push him off any kind of draw. Obviously my 4 kicker is weak, but I think this guy raises it up with the likes of J10 or J9, especially shorthanded. His flat call leads me to believe that he's on a draw, probably open ended and a flush. He's not a great player, but I don't see him calling a .60 cent bet into a .30 cent pot with just a gunshot.

*** TURN *** [Js 6s 5c] [10h]
Millr_HiLife: checks
dwfarrel: bets $0.60
Millr_HiLife: calls $0.60

I'm sure he's on a draw now, holding 74 or 43, possibly suited in spades. If he has top pair, two pair, or (very unlikely) a set, he probably would have seen my big bet on the flop as an attempt to get a free card on the turn, and bet out. However, this is where I feel I messed this one up. I bet .60 cents again, which is now a lot less than my .60 cent flop bet, relative to pot size.

*** RIVER *** [Js 6s 5c 2h] [8d]
Millr_HiLife: bets $1.40
dwfarrel: folds

If he had a made hand BEFORE this card, I think he checks again, since he's gotten good action from me on previous streets. Rather, I think this is one of the cards that I did not want to see.

Millr_HiLife collected $2.60 from pot
*** SUMMARY ***
Total pot $2.70 | Rake $0.10
Board [Js 6s 5c 2h 8d]
Seat 1: dwfarrel (big blind) folded on the River
Seat 2: OllieFitz folded before Flop (didn't bet)
Seat 3: hottoddy folded on the Flop
Seat 4: mr5375 folded before Flop (didn't bet)
Seat 5: Mastamune folded before Flop (didn't bet)
Seat 6: kamagong folded before Flop (didn't bet)
Seat 7: Retardo99 folded before Flop (didn't bet)
Seat 8: s8oy321 (button) folded before Flop (didn't bet)
Seat 9: Millr_HiLife (small blind) collected ($2.60)

Do I need to bet much stronger here on the turn?