Economies of scale prevent mass produced bikes for really light people. And I suspect that thinner tubes would be harder to work with and therefore more, not less, expensive. More generally, since most of the bike's weight is from the components, you would save less than you think by purposely targeting light people. It sounds to me that a compact size is important which leads me to believe that 16" (or under) bikes are probably a better fit for you.

Let's forget about price for a moment.

Do you actually need to carry the bike or can a bike that rolls well while folded satisfy your needs? Because if you need a Bromopton sized fold your options are minimal. If we forget about price, you could get a Brompton (S Model) with the titanium options and either a simple two (derailer) or three (internal hub) speed drivetrain that should handle most short rides less than 10 miles. From memory, it would be a little more than 20 pounds but if you installed the roller wheels -- I would pass on the Brompton option and just get some quality roller blade wheels/ball bearings -- you could roll the bike while folded quite well. And when it comes to carrying stuff, I think that the Brompton excels at the task since its bags/rack are integrated with the fold.

If the 1500-2000 USD for a titanium Brompton is too much, then see whether rolling a standard chromoly Brompton mitigates its weight. That would bring the price much closer to your target range. Although, if my memory is correct, the addition of the front bag with some other options like fenders would take you a few hundred past $1 K.

If rolling a bike works well for you and you are willing to accept a somewhat bigger folding package, you might want to check out the Bike Friday tikit. I test rode one at a local dealer and I thought that it rode considerably better than my old Brompton (or Merc). Then again, I am particularly sensitive to ergonomics and the standard set up on the Brompton didn't give me enough leg extension nor reach. I thought it rolled well and the rolling wheel would be considerably bigger on the tikit relative to the Brompton and consequently better across different terrains. If you went with a Model-T with some nice options (racks and stealth bag) it would take you to approximately the same price as the chromoly Brompton with nice options. If you ever decided to invest more money in the bike, you could shed a few pounds by upgrading components.

In my experience, bikes that are good at carrying things are far more useful than the alternatives. For folding bikes, that means can you fold the bike with the racks on and can I leave a bag on the bike while folded. Since these two bikes roll well while folded. My wife who is 5'4" and proudly 115 after having a baby thinks that a well-rolling folding bike for commuting is much more important than a light bike.

Decent cheaper options are the Downtube Mini and Dahon Curve.

You can fit a small rack that mounts on the braze-ons on the Mini's front fork. It is large enough to hold more than a pretty large seat wedge and can remain on the bike while folded. The Mini rolls well if you have a fold where the handlebar is in the interior of the fold.

I have never ridden a Curve. But enough people have written about it such that it will be worthwhile to test ride one since there are so many Dahon dealers. From what I gather, the Curve is probably better at carrying stuff than the Mini. Moreover, I would be surprised if it rolled while folded worse than the Mini. There was a thread that compared the two as a consequence of two forum members meeting in NYC (Caah and RHM, I recall).

Either of these two options would keep you well under $1000 -- unless you decided to go for the 8-speed Curve.