Will Synthroid make you gain weight?

My TSH is 4.03. From everything I've read, that is in the normal range, but still shows that my thyroid is slowing down. I've always thought I may have a thyroid problem. My father has a thyroid problem too. Anyway, I talked my doctor into prescribing me some Synthroid. I thought it may help me with symptoms and weight loss. I haven't filled it yet because after reading all of these posts, it seems that Synthroid makes you gain weight, whether it be water or fat! I do not want that. Is this one of the side effects? I feel like my metabolism is slow and I've always had to really work at losing weight. Is this worth taking if you're just having perimenopausal and possible thyroid symptoms? I do not want to gain!