It is not easy to get a precise answer, but the principle of one approach is:

Weigh the balloon. You should get a negative result, otherwise don't bother!

Weigh a vessel large enough  to contain the balloon.

Weigh the balloon in the vessel. Do a little arithmetic t make sure that all is in order.

Add a liguid or known density (water?) till the balloon is submerged. Note the weight. Mark the water level.

Remove the baloon, fill vessel up to the mark, then weigh.

A little arithmetic again...

Get the picture?

Weight an air-tight box with the vacuum set inside.

Then, put the helium balloon inside, and make the vacuum again. The balloon with fill the entire volume of the box (which should be somewhat larger than the balloon, but not too much or else the balloon would explode; but you can also include a mesh, a net, or anything that would prevent the balloon growing too big). Weight again.

The difference will be the mass of the balloon including its content, helium or else.

Neither of the above will work. The fact that helium is lighter than air and is bouyant in air does emphatically NOT mean it has negative mass. So the way which comes to my mind would be to get a completely empty balloon with a leakproof filling mechanism and measure its mass. Then measure the mass of the compressed helium cylinder from which you are going to fill the balloon. Carry out the filling operation without leaking or contaminating the helium, then when the balloon is full re-weigh the cylinder. Add the mass of the helium dispensed to the original mass of the balloon and you have your answer.

Another less accurate method would be to accurately calculate the volume of the filled balloon. Attach it to a sensitive spring balance and measure the upward pull of the connecting string. As air weighs about 1.1 Kg per cubic meter at sea level give or take a few grams for the barometer reading, if the volume of the balloon is (say) exactly a cubic meter and the upward force is 0.1 Kg, the mass of the filled balloon is , yep, you guessed it, a kilogram.

Turn the scales upside down and let the balloon push against it :)

Mass is not weight.

Place the balloon in a hangar so it is (just) floating. (This just protects it from wind effects - it does not affect the procedure.)

Fix a pulley to the hangar in line with the nose of the balloon. Suspend a large weight (say one tonne for a 100-tonne-ish balloon) so it can drop, say, 5 metres. Run a taut rope from the weight to the nose of the balloon via the pulley.

Drop the weight, and measure the time for the weight to reach the ground, accelerating the balloon with it the same distance (because the rope was taut).

Figure the acceleration a from s = 0.5 * a * t * t, because you measured s and t.

Figure the force F of the weight, which is g (9.81) * 1 tonne.

Figure the mass M of the accelerated bodies, which is (1 + X) tonnes.

F = a * M, hence M, hence X.

QED.

Unless you add slack ropes at the back of the balloon to restrain it, it will promply run into the pulley and deflate, so you will be able to weigh it empty anyway later.