I'm Alduin slayer and Volkihar Clan master yet I must still lug 60 kilograms (3x20kg) of Elder Scrolls around with me. The Dragon Elder Scroll, the Blood Elder Scroll and the Sun Elder Scroll. The game won't allow me to store them in my home chests. All three are needed in inventory for quests. Huh?

Does this mean there is a future DLC coming which will require them?

Harkon didn't carry any Elder Scrolls so why should I his killer, have to tote them around? Basically, I'm a light armored sneak of a vampire girl and all this weight detracts from my immersion, my roleplay.

I loved Dawnguard and still doing the radiants.

Very minor spoiler for Dawnguard side below about Dexion.

Quest items weigh nothing. Sell the Dragon one to Urag.

Sell it to the moth priest. I'm holding on to mine using the steed stone.

The Moth Priest is happy to serve me— I was Lord Harkon's worst nightmare.

Serving the vampires, Dexion offers no dialog to take any Elder Scrolls. The game says each weighs 20 weight units (pounds, kilograms, whatever). I doubt the 60 lbs is really adding to my encumbrance.

Next best thing is to use the Steed stone.
So no problem weight-wise now. I might speak to Urag anyway, since I have a couple of Unknown Books to hand over.

I should take all three scrolls to the White Gold Tower but I don't have transport to Cyrodiil.

You do not need to use the steed stone to carry weight that is not added to your total, none of those quest items you get stuck with add to the weight you are carrying. You think about it a bit you can easily test that out.

I know you can sell the Dragon one to the orc in the mages guild. I sold my one and had to buy it back off him when I went to do Dawnguard. He may buy the others.