Thinking more about Jim Henson's last Sesame Street segments...
The heavy and light game is one of the only times when Ernie initiates a game and Bert is actually excited about playing one of Ernie's games at the start. Nobody really knew that Jim Henson wouldn't have much time left (though I've seen quotes from people suspecting that Jim suspecting he'd die at a fairly young age), but if they knew, Bert's excitement over playing a game with Ernie (when he rarely wants to) could have had a little subtext - like knowing a friend or relative won't be around for too much longer and being excited to spend a little more time with them.
Then again, Bert's excitement also could have subtly reflected both Jim Henson and Frank Oz's busy careers. I used to wonder if they did anything together on Sesame Street during seasons 20 and 21, due to both busy careers, (and now know that some of their performances together premiered in those seasons), but Frank Oz did point out in 1989's An Evening with Jim Henson and Frank Oz that his directing career limited his involvement with The Jim Henson Hour (where Henson and Oz also barely worked together) and the recent seasons of Sesame Street, so it could be Oz being happy to have some time to work with Jim Henson again, after being so busy with his directorial career. And there have been a number of quotes that Henson and Oz usually improvised most of the dialogue from the Ernie and Bert sketches, so it could be Oz's own excitement as opposed to a writer putting it in the script.
Now knowing that "Best Friends Blues" came out in season 21, where Ernie mentions that Bert was suddenly sick, I guess it's great that it was Bert who got sick and not Ernie, otherwise that could have been a "harsher in hindsight" with one of Jim Henson's characters getting sick so suddenly. And it's also good that Jim Henson finally got to perform one of his characters interacting with Mr. Snuffleupagus, so close to before it would have been too late.
On the subject of another of Jim Henson's last segments, but no coincidence or subtext or anything, in the opposite game segment, Bert spends the whole segment being genre savvy, telling Ernie that he knows every time Ernie wants to play a game that Bert doesn't, he'll keep pestering him/roping him into the game anyway, and always happens to end right when Bert decides he wants to play. Which does end up happening here... Too bad Bert didn't decide to play then, knowing that's what would happen. Maybe it should have ended with Bert making a line similar to his "can't lose them all" from the drum beats game. Or maybe this was why he was so excited about playing a game in the heavy and light game - he decided to be enthusiastic from the start in hopes that Ernie would be ready to stop playing soon.