Since when is armor halved for tiny creatures? Also, Slight Build defines pretty well what it actually works with. IIRC, it's only for squeezing, opposed checks, and using weapons.
You'd want to be considered small, not tiny, when determining encumbrance. Small has 3/4 the carrying capacity, but tiny has a smaller multiplier (1/4? 1/3? 1/2? I dunno, AFB). Your armor would weigh whatever it would weigh for armor of its size, regardless of your size.