There will be some change in the feel of the tractor when using a rotating implement.
They are usually fairly well balanced so you shouldn’t feel like it is a washing machine with an unbalanced load.
With the tractor NOT started (of course) and the key in your pocket:
I would suggest that you look at the interior of the mower to see if there is something obviously missing or tied up. There is probably some sort of door thing hanging down in the front that can be lifted up to see the drum and blades that rotate. There could be a missing set of blades, a set that is rusted and can’t move, something tied up to the mower (manual, extra belts, extra blades…), or there could be something wrapped around the drum (string, rope, wire).
Did you cut the PTO shaft length to fit your particular tractor?