Well, this is not really my wheelhouse, but I know weight gain is a common issue with menopause. My wife is going through the same thing.
My best suggestion is to eat things which will uncouple your mitochondria. This will help turn some of your fat into brown fat. Brown fat burns more energy. It’s kind of like comparing a 12 cylinder Rolls to a 4 cylinder Toyota to go the same distance. Exposing your body to cool temperatures for a couple hours per day will also encourage production of brown fat. For me this means a cool house in the winter time. Or a cool swim for an hour or so on a daily basis can do it.
Things to eat to encourage mitochondria to multiply or uncouple are
MCTs
Omega 3 fats - ALA from flaxseed is one I recommend. Omega 3s tend to turn white fat into brown fat and activate it. (Lund, Larsen, and Lauritzen. Fishoil as a Potential Activator of Brown and Beige Fat Thermogenesis. Adipocyte, 2018; 7(2)).
Turmeric or Curcumin from turmeric - tends to turn white fat into brown fat. Curcumin in turmeric prevents the formation of the mature fat cells, thus obesity. Another way with which curcumin enhances weight loss is by transforming the white fat into brown fat.
Capsinoids from peppers cause the body to burn more fat through brown fat.
Wormword - there are several papers which discuss the mode of action of wormword via mitochondrial uncoupling.
Prolonged Berberine supplementation - Lingyan Wu, et. al. Berberine Promotes the Recruitment and Activation of Brown Adipose Tissue in Mice and Humans. Cell Death & Disease volume 10, Article number: 468 (2019). Here, we reported that 1-month berberine intervention increased BAT mass and activity, reduced body weight, and improved insulin sensitivity in mildly overweight patients with non-alcoholic fatty liver disease. Chronic berberine treatment promoted BAT development by stimulating the expression of brown adipogenic genes, enhanced BAT thermogenesis, and global energy expenditure in diet-induced obese mice and chow-fed lean mice.
Increase Melatonin - According to a 2018 study melatonin also has the potential to help increase brown fat in your body. You can increase your melatonin intake by consuming foods such as cherries, coriander, cardamom, tomatoes, and almonds.