It is accepted that heredity influences body fat. what does this mean?

It basically means you inherit fat genes from your ancestors. It has been known since 2007 that a gene called FTO was related to excessive weight gains and obesity. It wasn’t until scientists at MIT and Harvard University (published in the New England Journal of Medicine in 2015, I think) discovered that a faulty version of the gene causes energy from food to be stored as fat rather than burned.

Anxiety, stress, or something like that