Three bet turn?

[Maulik]

I could be against a better straight, not likely, we are heads up. I raised the last hand to $3 pf. I didn't make a c-bet; that would lead to a likely raise and fold by me...

Turn is nice, I want to build the pot w/ my straight + flush draw? So is the 3-bet necessary?

Party Poker No-Limit Hold'em, $ Hero (6 max, 2 handed) internettexasholdem.com

Button ($49.75)
Hero ($48.45)

Preflop: Hero is BB with A[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/club.gif[/img]. Button posts a blind of $0.50.
<font color="#CC3333">Hero raises to $2.75</font>, Button (poster) calls $2.50.

Flop: ($6) 2[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, Button checks.

Turn: ($6) 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $5</font>, <font color="#CC3333">Button raises to $10</font>, <font color="#CC3333">Hero raises to $20</font>, Button calls $10.

River: ($46) J[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
Button calls $25.45.

Final Pot: $71.45