I eat leansgain intermittent fasting style (16 hour fast/8 hour eating window), avoid added sugar from my diet, eat below 100 grams of carbs a day, and eat more protein and fat especially saturated fat. I do weights twice a week and cardio but I'm interested in HIIT as well. I did the advanced version of HIIT on my bike but whoa I wasn't ready for that lol.
Low carb, moderate protein, high (healthy) fat diet may work better for some than the traditional low fat diet. Reduce processed foods of all types.
Regular exercise as well as building physical activity into your daily routine should also help.
I also use intermittent fasting approach (restricting my eating into about an 8 hour period each day). This also helped a lot with managing my diabetes (I am lucky enough to be both hypothyroid and diabetic).
Not easy, but doable, with much effort. A bit thing that helped me was knowing that in order for me to lose weight I need to make much more effort than someone without a thyroid problem.
If your thyroid meds are adjusted like they should be and you don't have other issues, such as insulin resistance, PCOS, etc you should be able to lose weight, though most of us have to work at it. That means a healthy diet and reasonable exercise...