Is weight gain normal during perimenopause and wil this weight come off?

Sometimes, yes. Weight gain is a factor of declining estrogen ovarian production, decreased thyroid hormone production and metabolism, and estrogen conversion of androstendione to estrone from peripheral fat storage. Caloric restriction, and exercise is tantamount to reducing weight gain during this transition to menopause.
It is common. Because your metabolism can slow down, but if you have sudden or recent weight gain you should have an evaluation by your doctor, and have blood work to make sure you have not become hypo-thyroid which can make you gain weight and make sure your heart and kidneys are not causing water weight gain. There are a number of diets both fda and non fda u can do, i did the HCG and offer it to my pts.