Here is a Russian carrier VM-T "Atlant" used in a Buran and Energia space programs, which is perhaps the only airplane capable of carrying on its "shoulders" a load larger and heavier than itself:

Nuclear-Powered Lockheed Mothership

Nothing comes close in size to this unbelievable concept developed by Lockheed in the 1970s:



Note small "children" airplanes, attached to its wings... Its hard to imagine anything bigger flying in the skies, still retaining the shape of a common airliner. An aircraft of this size would have to land on water as a titanic "flying boat".

The Biggest Planes Flying Today

Unlike the B-29 and the B-52, which don’t show their size easily, the C-5 Galaxy would look insanely monstrous even on a postage stamp. To give you an idea of the Galaxy’s size, its wingspan is not just longer than the Wright Brothers’ first flight but the beast can also haul 180,000 pounds (which is about 90 tons). The C-5 was the world's largest plane when it was introduced in the late 1960s.

Arguably the biggest plane flying today, or ever, is Antonov An-225, a 6-engine beast that’s not only longer than the first flight in history but could probably carry one, two, or three whole aircraft museums. Numbers don’t mean much but here is an impressive one: the 225 can carry 550,000 pounds, which is 275 tons. Yes, you can say WOW.