This is the basic principle of bouyancy, which most folks are used to applying it when it comes to submerged bodies in liquids...of Fluids? Well, air is a fluid, so lets apply this principle to the ballon.
Bouyany Force = Specific Weight if Fluid being displaced X Volume of the object submerged in the fluid (note: this does not have to be completely submerged, as in the case of a boat that floats on water).
If you are talking about a Neutrally bouyant, you have to consider the dead weight of the ballon material itself. It may not be insignificant.
Obviously , hot air is less dense that the colder air around it, making it bouyant. But as the hot air ballon begins to rise, density of the surrounding air decreases, according to Pressure = Po exp (-gh/RT) where h is the height or altitude, R has constant, and T is the local Temperature.
So Pressure=pgh so Pressure / h = gives you the local density of the air, which you will need to see When the ballon goes neutrally bouyant, and guess what? That's when the driver, BLASTS the heat into the ballon to heat up the air, making it less dense and causing it to RISE.
When the ballon becomes neutrally bouyant, it means the weight of the Ballon skin (and its Cargo , OK) and the pressure force (pgV) of the of displaced local air at some height is about equal to the force of the pgV of the ballon (don't forget plus the cargo).
Hope this helps.
LightSpeed Dimitri, PE