I see the videos for telecom. Removing the junk upgrades the board. Where else does this apply? In the videos for mid grade peripheral some are shown with easily removable items, like heatsinks. Will removing upgrade the board, at least in some cases? Or is it just reducing the weight? For those who ship there must be more value in removing copper/aluminum.

General rule of thumb is reducing the weight and excess material worth nothing or ferrous items, will upgrade the board.
In cases where it's just empty space or the population of the board is small anyhow, it most likely will not upgrade the board.
The most items removed off boards in a way to "upgrade" them will be things like heat spreaders(sinks), transformers, plastics and steel.
This doesn't mean you can take any board and upgrade it like a midgrade to low perh just because you removed the junk.

It's the experience in this field where you can take a gold cap filled board and remove the chips and sell separately; or knowing when to remove flatpacks, ICs, and gold fingers on boards to increase your payout. If you're not consistently pulling in hundreds of pounds of material to scrap, it's not worth knowing what to do and what can't you do. Most ways to upgrade a board come down to the ratios of the post weight compared to what is being removed per pound individually. Always do your math or estimate before you do anything in thoughts of "increasing" your money.

Copper was what I was thinking of. Knowing to remove transformers (always?) is good. Unless it's a high category already? I realize now if the board pays more than copper alone, leave on, I would think. Anything to reduce shipping weight where I can get full price for locally without downgrading the board. Trying to find a place locally for boards.

I am curious about this as well. Especially when a board has integrated power supply junk and am considering cutting the power portion off.

I have the luxury of living near Boardsort. I believe the majority of people who send to BS, ship. In that case, removing unwanted items that "would not" upgrade the board but would reduce the weight for shipment; which in turn would increase your payout. If, you are shipping in, I would assume the best bang for your buck would be sending in only high dollar boards and finding a local yard for the low and med grades. Also, if the board is that low quality , remove the chips or anything valuable and save for a turn in.

Depending on the size of objects and removable items that NEED to be taken off, there are many that can be left on without touching and remains the same grade. Most heat sinks are removed.
It's better to get multiple opinions before removing anything because you could do more harm than right. 99.00% of the time , you leave it on. There's no map that tells you , "you remove this and it becomes this" or " I get this much more now ". It all comes down to experience and knowing every component to "know" what needs to be left on and what doesn't to hit the certain specifications for the class. Trust me, it's not worth the time/over effort. Best way to increase your pays, is to increase the amount of material you can bring in and get ready.