I'd be surprised that a heavier plane on takeoff exerts more force on the runway than a lighter plane landing.
And as the departing plane goes faster, doesn't the lift take stress off the runway?
Only for a short period between rotation and liftoff. Most of the takeoff roll is spent building up horizontal speed; the pilot doesn't command the aircraft to pitch up before it's ready to lift off.
Funily I was learning to fly at a grass strip and we were told to vary our positioning left and right on the runway for exactly this reason. In practice it meant that as we were taxiing to the runway my instructor would tell me “Today we are taking off left/right of center to avoid damaging the grass too much.”