A B-29 could carry 20,000 lbs over a short distance and low altitude. I believe they could have been used to deliver them in the ETO, but no '29s ever operated there during WWII, so it's a moot point. The B-17 or '24 were not even close to capable of delivering a Tallboy.
The US did some development on a similar bomb, but it was never used...They went straight to double-dog dare...Mushroom clouds-r-us...
Lancasters were used to carry the "Tallboy", but had to be modified to do so. I think 617 Squadron dropped the vast majority, if not all, of the Tallboys deployed.
The Tallboy was an invention of Barnes Wallis, the same guy who brought you the "Bouncing Bomb" used in the Dams Raids (Operation Chastise).
There was a bigger version, the Grand Slam, that weighed 22,000 lbs, also a Barnes Wallis invention. The guy apparently like big bombs..