A helicopter (which was explicity given as an example by the OP) isn’t capable of getting airborn on its own?
never mind
And your hypothetical five-year-old would be wrong. What do you call the force generated by an airplane’s wings?
Perhaps we should move on? The Saturn 5 lifts its own take-off weight of 3000 tons - impressive, but nowhere near the heaviest object ever lifted.
Building the Northumberland Strait Bridge involves a crane lifting a centerspan with a weight of more than 8000 tons. NaturalBlondChap lists a 16,800 t lift, which is 5 Saturn Vs and then some. (I’ve been looking for pics, so far w/o luck.)
Any other candidates in that weight class?
My apologies.
Here’s another candidate, depending on definition: Semi-submersible heavy-lift ships can submerge its cargo deck, get under a floating structure and lift it out of the water for transport. The MV Blue Merlin has transported a 60,000 ton oil platform.
Water I’d say can qualify as it is lifted by pumps to higher levels, though it is done a bit at a time.
Also explosives may have lifted up huge sections of earth/rock much higher then things mentioned here. Things like blowing out the sides of mountains for mining or projects like the Hover Dam might have imparted a slight upward force on the rock face before it came crashing down.
Underground and underwater nuke testing
By “helicopter”, I didn’t mean the helicopter itself being lifted under its own power, but rather that a helicopter (or small fleet thereof) would lift another object from the ground by means of suspended cables. I was thinking of a news report I heard about paleontologists cutting a mammoth out of a block of permafrost and airlifting it out by helicopter. The report said they had problems getting the mammoth out because it was so heavy.
Thread over! WE GOT A WINNER!!1 
Those aren’t singular objects. The OP asks for “the heaviest object.”
The east stands of old Mile High Statium in Denver were lifted by a thin film of water and moved outward for baseball games, and inward for football. If that counts, then this would be a contender for the OP.
If objects lifted by a thick film of water are allowed, here’s a serious contender.
How so? When has it been lifted?
Such ships are built in a drydock, then lifted by flooding the dock. Whether this counts as lifting for the purpose of this thread is debatable, though I think it’s probably as qualified as the stands at Mile High stadium.
Okay, but the next question is the light ship displacement figure for the “Knock Nevis”. It would be more than the 60,000 tonnes transport weight of the oil platform lifted by the “Blue Marlin” (per **Scr4’s ** post above) but what it would be I don’t know. Light ship displacement figures are notoriously hard to find.
There is such a thing as the world record for a heavy lift.
From http://www.cranestodaymagazine.com/story.asp?storycode=2031869
Chuck Norris’ dumbells.
Your link appears to deal only with cranes.
The 16,800 ton West Azeri top side was a jacking operation. It was jacked up and a boat sailed underneath it. It was then jacked down and the boat sailed the topside out to the platform location, where it was installed as a float over operation.
So it was lifted, just from underneath rather than a crane lift from above.
Heerema owns the worlds largest floating crane boat which has a lift capacity of 14,200t. It actually picks the object up from above rather than floats them up as in the heavy lift boats.
The S7000 largest lift was the Shearwater platform topside which was installed in the North sea.
See here - scroll down a bit for a picture.
http://www.heerema.com/Activities/RemarkableProjects/tabid/279/Default.aspx
However the current lift record is held by the slightly smaller S7000, lift capacity 14,000t, which in 2005 lifted 12,100 t Sabrather platform topside.
http://www.lr.org/News+and+Events/News+Archive/2004/Lloyds+Register+EMEA+assists+world+record+lift+for+Sabratha+topsides+installation.htm
http://www.heerema.com/Activities/RemarkableProjects/tabid/279/Default.aspx
Picture here with the S7000 in the background.
Both the S7000 and the platform topside may be described as, rather jolly large.
Indeed they did. As every science fiction fan knew, rockets do not “lift off.” They “blast off.”