Every 3 feet? I think you could park trucks on top of it. Well... not literally, but it would definately be strong enough.
A couple of things you'll probably run into is the 4x4 stock may be twisted. Make sure an eyeball them as you pick 'em at the store to make sure you get straight ones. Another thing is the bottoms of the joists may not be even. Get some dry shims (wet shims will shrink as they dry) to support the higher joists. Also, a small dab of glue will keep them from slipping out over time.
What are you using for posts?