What is the maximum weight on the main gear of a large aircraft at rotation and touchdown?
There's more weight on the main gear when the aircraft pushes back from the ramp and is taxiing than on the takeoff roll, due to the lift generated from the wings. When the aircraft rotates the higher angle of attack generates enough lift to 'offset' the aircrafts weight and it takes off.
The most weight a main gear set will take will be on a firm landing at max landing weights (or above in an emergency). On the 737 there is a 'hard landing' G limit of (i think) just over 2G. So in theory temporarily on touchdown the main gear between them are handling twice the aircrafts weight.

As an example for the 737:
MTOW 77 tons.
MLW 65 tons.
4 main gear wheels.

heavy take off = 77/4 tons when parked ready to push back, reducing to 0 on rotation. 
ie roughly 20 tons per wheel and tyre.

adding in landing G forces...

firm landing (but in limits) = (65*2)/4 tons on touchdown, quickly reducing back to 65/4.
ie roughly 32 tons per wheel down to 16 when parked up.

emergency landing after take off at MTOW = (77*2)/4 tons at touchdown. 36 tons per wheel!