If your vet didn't do any bloodwork before putting Sugar on thyroid medicine I would guess that the thought process was less about a thyroid issue than it will help with possible IR control and weight loss.  So you know, while the use of thyroid medicine can help jump start weight loss, it will do nothing to help control insulin levels.  However, since Sugar has been on it for over a year now you would need to wean her off it slowly to allow her thyroid to start functioning again without it.

Looking at her crest there's no doubt in my mind that Sugar is IR and needs tight diet control, but getting bloodwork done will give you a baseline for where you're starting now compared to where you get to once she's no longer free feeding and getting closer to her ideal weight.