What's the mechanism? It can't just be separation from the atmosphere -- if you fill a balloon with helium, it will get lighter, not heavier. Same thing if you fill a cylinder that sinks in water (perhaps because it was already full of water) with atmospheric air; it may well start to float.
Suppose you have a balance scale with a "cylinder" full of air on one side. You pump out the air and put in helium. What happens to the scale?
That's because the weight of the gas cylinder is relative and you got the point of reference wrong: The base weight is when it's a vacuum inside the cylinder, because otherwise it doesn't even displace the air which you don't want to measure for your reference weight, making it appear heavier. Whatever you add inside the gas cylinder now will make it heavier and the difference you get is the weight of the gas.
While I appreciate the answer, it's not a great explanation of the balloon example, since a balloon starts out effectively containing nothing. The problem there is that as you add helium, the volume of the balloon increases.
I'm a little more comfortable with saying we do some weighings in a vacuum (say, to determine the density of air at a given pressure) than with saying we'll start with a cylinder that contains a vacuum. For example, our 40kg cylinder, when airtight and containing vacuum, will weigh less than a 40kg object should, and I think that muddles the example.
Only the difference between vacuum cylinder and helium cylinder matters. (Since the buoyancy in air only depends on the volume of the cylinder, not what's inside.)
An empty cylinder should measure exactly as much lighter than the air as the air weighs. That point is your zero point.
Put in helium and you'll eventually reach and exceed the parity point as you keep filling up (same weight as the air), and the ratio of how much it moves for x volume of additional filled gas tells got the additional weight.
Soon enough you'll reach 2x air weight and you'll have tipped the scale exactly.
What's weight? Mass is well-defined; you could call weight "the force of gravitational attraction between the object and the earth" or you could call it "the force acting upon the object, when at rest". Since we're talking about measuring weight, I was using the second one, which is easy to measure directly.
Granted, I was also using the first sense when talking about the weight of the helium specifically. I guess in that sense my terminology could have been better.
Suppose you have a balance scale with a "cylinder" full of air on one side. You pump out the air and put in helium. What happens to the scale?