I see some guys bouncing up and down a lot when they're out of the saddle. Some guys are bobbing their upper body when they're really straining, sometimes left and right as well. I think it would be better for them to have any extra weight on the bike as opposed to their bodies.

This. Yes, when accelerating, you can count the mass of the wheels almost double, but this is a small effect and as pointed out, not when the bike is moving at a constant speed. Rolling resistance differences between different tires is a bigger effect.

To the OP: you've asked the question, it's been answered. Sorry you don't seem to like the answer, but fortunately science doesn't care whether you like it or not.

Here's what you should take away from the video: its wrong. More specifically, here's a great example of how a power meter in the wrong hands is a dangerous thing.

Heck different sport but as a positive bit of training. I used to swim competitively. For the really big meets one would shave their legs to minimize drag. It works, but no coach I have ever known or known of encouraged shaving for every meet. The idea was to get an extra pop for the meet, it helps top feel fast.

I can see the same advantage riding. Shed the extra weight and now you feel better on that hill.

Any rider who has done an unsupported tour knows that it is better to have any extra weight on the bike and as low as possible, evenly distributed of course.

If nothing else think 100 extra pounds on your body and what it would do to you, heck even if you are just sitting on a stationary trained and not pedaling.

Body weight and bike weight both matter, but not equally.

If you take stuff off the bike and put it on your body (e.g., taking your tire kit from a seat bag to your jersey pocket), the total weight will be the same, but the weight moved from the bike to your body will go from being unsprung dead weight to sprung live weight that you can move around as you ride. Within reason, this will make the bike more maneuverable and ride better. It will probably subjectively feel more "alive" under you and easier to handle. But on the downside, you will now have this extra weight up higher and on your body where it may be uncomfortable or even dangerous. (The extreme of this would be to take 40-lbs of camping gear and move it from panniers to an expedition-style backpack on your back.) Most non-touring cyclists balance these two factors and do whatever is convenient - they'll put their tire kit, tools, water, etc. on the bike, and stuff a windbreaker, snacks, etc. in their jersey. I think what is comfortable and convenient trumps the physics here.

Then there is the donut you put in your stomach. This also adds to the total weight, but extra weight you carry on your body is also extra weight you carry around all day long which increases muscle mass - a unfit 300-lb person will probably have much more muscle mass than a fit 150-lb person. That doesn't mean the 300-lb person will climb as well as the 150-lb person, but it does mean that being 20-lb overweight is better from a bike performance standpoint than putting 20-lbs of lead in you seatbag. (Obviously, the reverse is true with respect to one's health.)

One thing about ultra-light bikes and gear. They may be more expensive and people probably obsess too much about bike weight, but a 1-lb lighter bike is a a pure win - there is no downside (other than cost).

- Mark

I'm curious about that. Do you have further information handy?

One thing about stashing "stuff" on the bike is that I don't haul it up & down with my body/clothing weight each & every time I get out of the saddle as if it was in my jersey pocket. A few energy bars& gels, OK. Add your flats-kit, a rain jacket and a water bottle or two and I'm not hauling that up/down every time I stretch, accelerate or climb out of the saddle. Easy enough to fit the proper size seatpack for a ride & stash what's needed. I'm not hauling a load of bottles from the team car to my pampered leader for a minute or two, it's my tired old back in less dramatic situations for hours on end.

-Bandera

full touring load for a 6 month trip with some overpacking I think then 23 years ago,
the bike and kit weighed more than I did.

Bike weight makes huge difference just went from steel to carbon massive change, climbing uphill is a breeze now, on the steel one I thought I'll get a heart attack lol