I lost 10 pounds in 3 weeks a few months ago realizing this and how it happened was weird. I was playing Injustice 2 and if Robin and Batman are pitted against each other, they exchange some words pre-fight and it went something like this:

Batman: "The League didn't teach you everything."

Robin: "And what exactly did they miss?"

Batman: "The importance of self-control."

This made it all click. My attempt at weight loss was always about exercising hard as shit, but I never fixed the most important part, which was self-control over my eating habits. The Bats helped me understand that it's my emotional attachment to food and my lack of control over it instead of the amount of time I kill myself at the gym.

Mental health is definitely important for weight loss, but then again, mental health could be important for all kinds of change and improvement.