I ride a 16.0 hand quarter horse and I've ridden a 15.2 arab with NO issue. You weigh significantly less that I do, so I don't see a problem. The quarter horse has absolutely no issues what so ever carrying me...
Here is a good article about horse and rider size/weight bearing capacity: EighteenHands ~ How Big is Too Big? (The Great Weight Debate)
There are also 2 other articles referenced in that one. You can additionally do an internet search for "How much weight can a horse safely carry?" and ALOT of literature comes up.
A 16HH TB should have no problem carrying you. If the horse's rider is consistantly someone who is skinny, it just may be a matter of getting the horse used to extra weight (conditioning and easing into it before riding hard on the horse).
Often times thin poeple are not educated about weight issues and just need some information. If you can present material to her in a polite and professional way she may re consider....and you'd have opened her eyes up to the fact that big girls can ride too.
At the end of the day some poeple are ignorant and closed minded to larger riders but hopefully this person isn't one of them.
Best of luck
Send her to my website or facebook fanpage...I have some videos of large riders competing in professional level cross country, low level dressage, and horse versatility games....she can see first hand that horses CAN carry 180 pounds, no sweat
Best of luck....and let us know!