...It's not about the protagonist actually being 'fat', but lazy.
When the Ex at the start says "Aren't you sorta... fat?" she's using it as a way-in to end the relationship 'cause she doesn't like how much of a 'slob' the protag. is. The heroine's so insecure and afraid of failure that she quits everything she starts the moment it gets hard, so she reacts out of anger at the Ex (partly because she literally isn't fat, but mainly 'cause she's insecure about her lifestyle), but winds up proving her right when she gets bored of exercising.
Being 'fit' becomes a cypher for simply being wanted or loved, which is compounded by the way she reacts to the athletic girl ("And those abs...!"). When she says "Running doesn't get you slim at all." she means 'Gets you noticed' as much as anything - having not lost any weight comes second, referring to how her attitude hasn't changed (and she partly knows that's why Athletic Girl ain't noticed!).
The protag. lashing out with 'You run 'cause you've got nothing better to do!' is inward facing; she feels Athletic Girl is an arrogant jerk ('cause she's hot) whilst feeling insecure ('cause she don't feel hot/ain't noticed). In the end it's revealed Athletic Girl liked her for who she was anyway (as someone that didn't care if she did get fat), and the subsequent epiphany makes the protag. feel like Athletic Girl will be the one to help her confidence so she can finally change her outlook/lifestyle for the better (which she's always wanted).
...or something.
I liked it, anyhow. Hope there's a sequel. C :