The AE86 is posted, factory in the U.S., around 2300lbs.
The dimensions of the FT-86, so far, are extremely similar (almost exact) to that of the AE86, with it actually being an overall shorter vehicle, yet slightly wider.
Take into consideration lighter materials on the mechanicals (all aluminum engine, compared to cast Iron/aluminum 4A-GE, etc.)
Take into consideration stricter safety requirements...
Eh, I'd say ~2600lbs
2800 is really pushing it...
The pictures don't do justice to the size of this car, it literally will be as small as your current AE86 (if you're lucky enough to own one
).
Edit: For those who are picky about the weight, just do what I'm gonna do: Baseline model in terms of luxaries without skimping on the performance. If I can get all the performance goodies without power windows, locks, sunroof, GPS gizmos, etc., then I'll be as happy as can be.