I won't claim to know diddle about training to ride a bike, I just ride. I've been riding since 1971 and I've never made any team. Never wanted to.
That said, I can see some possibilities in using weights at certain times. Most sports training methods use weights at some point or other. Why wouldn't cyclist's? With the very little that I know I can see where it would be pointless for endurance training, but could easily pay off in strength training. Limitless endurance with no strength won't get you very far.
If you're climbing with more weight, then you may not go as fast but you are working harder to go the same speed. More weight = more gravity effect. Could choose a steeper hill I guess.
If you are on the flats with more weight and want to "pick it up" you've got to work harder to do that (inertia).
I would not put it on the person. I would put the added weight on the bike. Add some panniers (sp?) loaded with rocks or lead shot and go for a ride. Tell me that wouldn't be a work-out. Then take the panniers off and watch what happens.
I would bet that that at the higher levels that the training bikes are nowhere near as light as the race bikes. Unless the budget is unlimited, just from a longevity point it wouldn't make sense for them to be so.
I used to swerve around my hallucinations, now I drive right through them.