Its really going to depend on a lot of things. First of all, how you carry your weight. Just because you are overweight doesn't mean that you are necessarily an unbalanced rider. Obviously though, if you are bouncing and flopping all over the place, it'll bother the horse more than a 150lbs rider bouncing and flopping.
The other thing to look at is the horse himself. Does he have good bone or is he fine? Is he sturdier? Shorter backs tend to have higher carrying abilities.
Finally, what exactly are you doing with the horse? 90% of horses could probably carry 250lbs on their back for an hour without much problem at all. Different story all together if you're an endurance rider and riding 6-7 hours over rough terrain
I also struggle with my weight quite a bit. I picked a horse that I KNOW can carry me without difficulty and work from there. Riding is a good form of exercise for the rider as well, so don't give it up :)