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So the bad news is you wont find anything under $120 (I'm assuming USD) that's designed to support your weight. If you do find something comfortable it will probably wear out quickly. If you're willing to go a little more expensive though, you can get this chair for $192 on Amazon right now. This is the chair I used for several years before switching to a standing desk. It's designed to support someone up to 350lbs and the armrests are wider apart than most chairs so you won't be cramped. The frame is all metal and feels extremely sturdy. It was the only sub-500 dollar chair I've ever used that I could sit in all day without problems.
EDIT: I'm 6'4" and ~280lbs, so I say the above as someone about your size.
I've been looking at this: [link]
I'd even consider the DX Racer even at its high price if I could get a cover for it.
My next chair is going to be something like this. Double plush, wide, and simple design. I like a lot of cushioning for gaming sessions.
Im 6'0 and 330. I've had this one for a year or so and am pretty happy with it.
This is the new one