Thin privilege is being allowed to work out for yourself what your priorities are in life and how much time, money and effort you want to put into different things. When you’re fat people assume that losing weight should be the absolute top of your priorities, and say things like, “But you can change your body! Sure, it takes hard work and discipline, but you can do it!” — the assumption being that fat people who don’t lose weight are lazy and should be abused for it.
A thin person can put time and hard work and discipline into learning Urdu, or writing a novel, or starting up your own business, but nobody calls you lazy if you don’t want to do those things — they just accept that you have different priorities. Why can’t they accept that fat people might have other priorities than putting everything they have into making their bodies a bit smaller?