Having a cut-off weight set at 150-170 is pushing it way too far, IMHO. Heck, I am not big by any means, but by the time you add in tack, the amount my horses carry on a daily basis is over 175.
Now, on a person that was bigger, whether they were permitted to ride at my barn (it's my personal barn with my personal horses) would greatly depend on which horses I had available and what their riding level was. I only have one appropriate horse for a heavier stark beginner. However, if the person is a fairly competent rider, I have a couple more that could carry heavier weights (I would go up to about 275 for them). If the person was very experienced, I have a horse I wouldn't hesitate to put 300+ on and soon, I will have another that can carry as much or maybe more.
For somewhere like a lesson stable though, I can understand them setting weight limits because, often, it takes too much time to figure in the additional factors of whether a certain horse can carry this certain person who happens to be heavier.