hot rolled, mild steel 2" square tubing
wall thickness of .125"
(length from reciever to channel is 30")
the platform weighs about 30lbs, and the bike weighs about 215lbs.

From this, I ran one of the web beam calculators using
as a calculation load 250#, and got just over 1/8" of
bend, and 13.6 ksi bending stress at the receiver.

With a yield stress of 36ksi, A36 would seem to be OK--BUT
it is not unusual for bouncing and other momentary
stresses to cause the actual forces to exceed that, so
a common rule of thumb is to use four times the load for
a safety factor.

If we re-run the calculator for a 1000# load, we get just
over 1/2" of bend and a stress of 54ksi, which would put you
over. So my quick "back of the envelope" calculation would
agree with your other two responses, use the thicker section.

--Glenn Lyford