You cannot increase your metabolic rate without putting on weight, whether that be of fat or muscle. In terms of changing how much you weigh, it's strictly calories in and calories out. A doctor even proved this when he ate nothing but sugar and ultra processed snacks, and still lost weight
Athletes can get way more calories than the average person and not put on fat because they burn a lot of their calories through the athletic activities that they do, and because most of them are on strict meal plans, whereas the average person has no sort of structure to their diet. not only that, but a lot of athletes actually take extreme measures like self-starvation prior to certain events). Genetics also play a role in metabolic rate, but obviously cannot be influenced by your lifestyle