I'm very late, but the answer is: kinda. The heavier you are (in terms of fatness and what you've eaten) compared to your strength, the more stamina it takes to move around. Internally, there's a threshold where you can be classified as "immobile", but it doesn't prevent the player from moving around (otherwise you'd get softlocked!), and only comes into play in some niche narrations. If you're curious as to whether your character is considered immobile, you can check your status/narration - if your walk description starts with "slowly", or your status page mentions "You're starting to feel rather slowed down by your weight.", then you're immobile by the game's standards ;p