Mulberry or catalpa would get the vote here for a fast-growing tree with decent limb structure - don't know if either are suitable for your location - but, at 10, your son will likely be long past any desire to build a treehouse by the time one planted now is of sufficient size to accomodate more than a board or two.
Paulownia - not a chance - yeah, it'll grow 10+ ft per year, but it's just a beanpole.

The weeping willow.

My neighbor planted one seven years ago that if pruned right would hold a tree house for a bit. But man, it is NOT a tree for every lot and not real long lived.

Any common ground near by?

Thanks everyone! I was afraid we wouldn't find something that could grow super fast AND be weight bearing.... Richard, I really like your idea of building a raised "fort" and planting trees around it to give the same feel :0).

You know, some ivy vines growing up those poles to give the camouflaged, jungle look, could also have some appeal.

Richard.

Kids can't have everything they want, lol. He'll have kids of his own by the time you can grow a suitable tree.

How about a tent or lean-to fort? Great fun. Stone fire pit.

Cottonwood, Catalpa, or Weeping Willow probably best bets. All of them are somewhat moisture loving and perhaps not the best bet for your area.
Our Southern Yellow Pines are fast-growing. An equivalent for you would probably be a Pondersa Pine.
Like Richard's idea also.

Richard, you are a true boy at heart!!! LOVE the ideas :0).

True that kids can't always get what they want, but if it is within my means and isn't an unreasonable request, why not try?!? My 8 year old daughter would even love the idea of ivy growing up the poles and would probably have just as much fun as my son!!

The local garden company is recommending a fruitless mulberry tree. I like the way the branches twist and spread, so that might be the way to go!

Thanks again everyone!!!!! Thanks, Richard for you brilliant ideas :0)