I've read through this entire post, grappling for the issue here.
Based on your responses, it would seem you both have issues with each other - you dislike his brown nosing, over-eating, incompetence... And he dislikes your bicycling.
What is it about his ridiculous dilapidated tricycle picture that personally offends you? Me thinks you take the bait my friend.
And what's with the fat jokes and pictures? Don't go there at work... ever.
And don't offer to "help him get in shape." how insulting.
Take the high road. The resulting fallout always makes the other person look stupid.
Guaranteed.