TT vs. consistent open-raiser

This is my first starting thread post, so please excuse any posting etiquette oversights or even the simplicity of the post. Also, for clarity, I am seeking any advice on how others would play the hand in question differently pre-flop and post-flop.

Here goes:

Play is on Bodog 2/4 NL. Play at the table has gotten pretty loose, and I as a result have tigthened slightly (I have a very LAG reputation at these tables).
Here is the needed player-specific background - Villain has only been at the table for about 2.5 orbits and raises preflop frequently to $14, including three consecutive pots to $14 preflop. I played one of the past three hands with 55 and hit an easy man's straight and he paid me off for over $100 of his stack (roughly $70 of which he put in after I made my straight on the turn) w/ A7 os on a board of 4678X. One other hand was shown down where he open-raised like this, which he won with KT offsuit.

On to the hand in question...

Approximate stacks are as follows:
Villain - ~$340
Hero - covers (~$850)

Villain is UTG+1 and makes his standard raise to $14 (4th consecutive hand where he has open-raised to this level).
Hero is MP (3 seats behind Villain) and raises to $35 with TT. This is the first time anyone has challenged his opening bet with a raise.
Table folds back to Villain who minreraises to $56. I'm not entirely sure what this means, but I'm sure it means he's better than A7 o/s or KT o/s.
I call, pot = $118

Flop:
J T 7 r

He leads out with $100. I think (ok, pause) for a few seconds before I raise to $200 (I know how much we all hate the minraise, but my thinking here was that given stack sizes, he's either folding or pushing right here, so the only action I don't want to make is a flat call). He pushes for his last $180 or so, which reraises me $80. Of course I call...

Thoughts? Different lines along the way?

[Raven]

Just push the flop, for the rest its standard for me.

[JFB37]

Although minraises are much maligned, in this situation I rather like it. Because villain is short-stacked, there is not a huge difference in the odds hero is laying between raising to $200 or to $280. Hero's goal is go get all the money in and, at these levels, this may have a slightly higher chance of success than a push. Villian may think that the minraise is a cheap effort to get a free card on the turn with a straight draw.

Of course, Villain might think that a push is an effort to get two shots to complete a straight draw.

Or Villain might not have a relevant thought at all.

I think you played it fine.

[Dubra]

I like it. Your minraise usage and explanation seems good.

On to the outcome, not that anyone cares given the limited replies posted.

Villain did have a real hand with KK and hit a K on the turn, but I was satisfied to get him all in while I was a 9-1 favorite.

I'll make note of better/tricker questionable/worse plays during my next session for future posts.

i think you played it perfect, actually.

[SpeakEasy]

I think this play was fine, given his stack size. Push rather than mini-raise also works here.