On my
tongue strength page, you'll see 1-1/2"x1-1/2"x1/8" angle listed, but not 3/16". 3/16" has a horizontal/vertical capacity of 2,700lb-in, which is fairly weak - it's about half as strong as the tongue members on a HF 1800lb trailer, for example.
If we allow the tongue to be half as strong as the Aussie rules require (which I think is reasonable for a teardrop) and you want a tongue that's 36" long, two of those 1-1/2"x1-1/2"x3/16" angles would be sufficient for a 600lb GVWR teardrop - so that would be well under 500lb unladen.
If you think you can build that light, those angles would be borderline. Even if the angle is strong enough for the A-frame, you run the risk of getting a frame that bounces (vertically) because the 1-1/2" angle won't be very stiff. However I don't doubt the angle would be strong enough for the rest of the frame.
If you want to follow madjack's good plan to add a stronger central tongue member, you'll need to attach it to two widely spaced crossmembers (say, at least 36" apart) otherwise you run the risk of the tongue bending the rear crossmember.
Andrew