Sure, there’s several ways of doing this. For example, if you take a bag of sand and weigh it, then tie the helium balloon to it and weigh it again, it will weigh less with the balloon attached. The difference in weights tells you how much helium you’ve got, and from that you can work out how much that helium actually weighs.
Quite easily, and it’s a great experiment to do at school!
First, dunk your helium balloon and dunk it into a big tub of water which is full to the brim. Collect all the water that spills out and put it in a measuring jug to measure its volume in litres. This is ALSO the volume of balloon!
Next look up the air density: it changes with altitude and temperature, but in normal, British pressure and room temperature it’s about 1.2grams per litre. Multiply the air density with the volume you measured to give the mass of displaced air. Again, it’ll be something like 1.2grammes.
Now tie a string onto the balloon and tie some little plastic beads onto it. Stop when you’ve put on enough beads to JUST hold the balloon down. Congratulations: you’ve counteracted the buoyancy trying to float the balloon away!
Now let all the helium out of your balloon ( 🙁 ) and put the whole balloon-skin+string+beads assembly onto an accurate scales. It’ll need to be accurate because the whole lot will probably only weigh less than one gram!
Finally, subtract the balloon+string+beads mass from the displaced-air mass to give the mass of the helium! What a fun question 😀