Your concerns are valid, definitely! Though, I think changing your mindset on the matter would make this more of an awesome opportunity than something to be afraid of or worry about. I've been to plenty of gyms where the employees are overweight, and honestly, why should it matter? The gym is to get in shape and be healthy, so everyone should be there. Plus, like you said you can use the facility at no charge! I feel really uncomfortable when all I see are people who look like they spend 6 hours on a treadmill, and I feel more at home and like I can be myself when I see people on the same page as me.
Sounds like an awesome opportunity, take advantage of it and have confidence!