No, sorry, that’s not correct. Horse racing under saddle takes the weight of the rider into account, but not harness racing – read the link I provided above discussing drivers’ weight and the physics of sulkies.
Beyond the racetrack, most equestrian sports do not in fact factor in weight. Showjumpers clear amazingly huge obstacles whether their rider is a petite woman or a tall man. Men and women compete as equals whatever their size in reining, cutting, polo, barrel racing and other such sports where athleticism decides the contest.
One equestrian sport did in the past have minimum weights allowed – combined training, also known as three-day eventing. In that sport, the horse and rider combination do a dressage test on day one (think of it as like the compulsory figures in figure skating), on day two gallop cross-country jumping fences, ditches, banks and other obstacles (the phase in which Christopher Reeve was crippled), and on day three do a round of showjumping. The winner is the horse/rider combination with the fewest faults over all three days. At the highest levels it’s a gruelling test of skill, strength, speed, and stamina.
Until 1998 there was a set minimum weight for the rider under international federation rules. This rule has been rescinded.
So, which way was fairer – a minimum weight, or none? As a rider I can attest that it makes a considerable difference to a horse whether the load on its back is live or dead. A skillful rider can move with the horse so as to minimize the effect of his/her weight. A heavyset rider of great skill will burden a horse less than a skinny person who doesn’t know how to ride well.
So for horse sports, weight does matter, though not as directly as you might expect. And yet very few equestrian sports require any minimum weight standards.