I know nothing about your student but she may actually have a genetic predisposition to be larger, and may always be.
More important than the size of the seat is going to be the balance it gives her, which is going to have a lot to do with the rest of her proportions.
That being said, I think people tend to buy saddles that are too small for them when an 18 or 18.5 seat may put them in a better position. I personally have an 18" jump saddle, and an 18" dressage saddle and they weren’t hard to find at all. I found them both on consignment at Middleburg Tack Exchange and there were a lot of options in that seat size. My dressage saddle is an older County Competitor and it was very affordable and has a pretty flat seat.
Someone mentioned a draft or draft cross but presumably she wants to keep the horse she has and in any case, drafts can be a bad choice for larger people if they have longer backs or funky conformation. They were originally meant to pull, not carry a rider. What’s going to be the most important isn’t, in my opinion, losing weight, but making sure she has a good core and the correct balance. (remember, people CAN have muscles hiding under extra weight they may be carrying!) Also remember a woman, especially a shorter woman, who looks heavy is probably the same weight as your average male rider.