I would also recommend a small fiberglass trailer - Scamp and Casita. Oliver is expensive, as is the Escape and I don't think they are very light. Bigfoot is a fabulous trailer, but is also very expensive and the smallest Bigfoot is 4300lbs GVW - that is not light.
We have a 13' Road Runner by Sun Valley with a GVW of about 3200lbs. It is small and fits 2 perfectly. I think you could move up to the 16' and still be under 3500 lbs, but you'll have to be careful when deciding on your options. Options can really add to the weight of the trailer.
Other small campers that could come in under 3500lbs (when being careful with options) are FunFinders and Coyote (Jayco?). The 16' FunFinder even has two very narrow bunks in the back and a dinette that makes into a queen bed. It is the most sleeping space I've ever seen in a 16' trailer. The bunks are only 26", so in my opinion they are only suitable for a small child.
As smaller trailers become increasingly more popular as the cost of fuel rises, many big manufacturers are coming out with 16' light weight trailers.
We have an Escape. I think it's a little more than the Scamp or Casita but the quality is excellent and you don't have carpeted interior walls. Under 2000 lbs. It's also not as wide as the bigfoot, which I prefer. My parents had a Bigfoot and I didn't much care for the layout or the width..... check out the fiberglassrv forum, there are los of little trailers to consider.
My 16 foot fun finder weighs in at 2100 pounds, figure wet at about 2900, it handles like a dream but we do pull with a full size Chev truck. Used I paid 6k and it was 3 years old. It has everything but the bathroom sink, and you can use the kitchen sink for brushing your teeth.
Just like to keep the info straight. The Oliver's base dry weight is 2400 lbs,(including a full shower/bath)and plentiful standard equipment, with a 3500 GVWR. The rugged, all aluminum rust-free frame helps balance the extra weight of the double hull, and extra base features. A full bathroom, with shower, is included in that base weight, unlike the Escape 17, where adding just a shower adds 200 pounds to the "under 2000 pounds" advertised. Neither of these trailers, nor the Casita or Scamp, would be considered heavy trailers by most people.