I've taken Synthroid since 1995 for hypothyroidism. Even with meds and my TSH in the normal range, I was obese until 2001, though I desperately tried to blame my failure to lose weight on my thyroid. Nope, it turns out it was just me eating too much and being lazy.
My unsympathetic doctor (I love her!) told me that once my TSH was in the normal range, I could lose weight like a person with a normal thyroid. And darn it, she was right! Once I took my head out the sand, started counting calories, and joined a gym, the weight came off pretty fast (122 pounds in a little less than a year).
So, no you won't gain weight on Synthroid. Once you get on the right dosage (and it takes time and tweaking), it will help you immensely with your weight loss efforts. We have at least four successful maintainers in the Maintainers forum who have lost -- and kept off -- large amounts of weight while taking thyroid hormone for hypothyroidism.
So don't worry about taking Synthroid. If it turns out that you're hypothyroid and need it, it could be the best thing that's happened for your weight loss efforts!
PM me any time with questions or if I can help.