lightest 3 person double wall tent for $250

It depends a lot on how much space you want. There's a wide range in actual living space in tents that are designated as 3-person.

The Easton Kilo 3P is $199.75 at backcountry.com if you use the current coupon. It's a flawed design in several important ways in my opinion, and actual trail weight is around 3 pounds, 8 ounces, not the weight you see listed.

Maybe it's best to look for a used Big Agnes Copper Spur.

The Golite SL3 would meet your specifications.

The Sl3 is very tight for 3, perfect for 2.

The previous generation REI Quarter Dome 3 is on the REI outlet website for $269.73

You can also find a previous generation MSR Mutha Hubba for about the same price, though it would be heavier.

I saw the BA Copper Spur 3 on SAC a couple weeks ago, at $250. Under 4 lbs. Maybe last years model is available somewhere for similar price. I have the 2 and really like it.

Dang, that's cheap. They updated the copper spur ul 3 so last year's model should be going cheap thru the spring.

Save up a little more and get a Tarptent Hogback. :)