I know that for airships, the maximum practical size could be limited by factors like air resistance, the danger of a collision with the earth when landing, the need to build huge hangars, etc. But for a tethered balloon that is designed to remain in one location rather than fly from place to place, and which could be held stable by tethers when landing, and which would need at most only one humungous hangar, what might the maximum size of such a balloon be?
The weight of your balloon won't be an issue.. size could be 80km or so
Supposed the balloon is filled with a gas that would normally leave the planet atmosphere, e.g. hydrogen, its own weight would not limit upforce inside the atmosphere. It can always be designed in such a way, it can carry its own hull. Surface of the balloon goes 3th power, volume (which will decide the lift) will go 4th power. When it would not be attached to the surface, max size at first glance will be the height of the atmosphere that can provide a lift (say 80km).
Pressure of the gas inside the balloon
A limiting factor at stratospheric heights and above is inflation of the balloon. The higher you go up, the lower the external pressure will be and the more pressure your balloon hull will get from the gas inside. The balloon gas will want to escape. This could inhibit your balloon to penetrate too deep into space. Of course, you could add (much) more balloon material, like it is done with weather balloons. This will increase the weight of your balloon without it gaining extra volume. Stratospheric weather balloons don't enter space.
A challenge will be the tether cable
When the balloon is huge, but smaller than the height of the atmosphere, you'd need a long tether cable. That must be very strong and very firmly anchored. I think the max size of your balloon will be such, that it sticks out into space, balancing forces, to lower the pulling force on the tether cable.
On the other end, a tethered balloon should maintain enough pulling force, to keep its tether cable in a vertical position, else the tether could bend and break. To achieve that, your balloon should be able to carry multiple times the weight of its tether, and the tether cable should be able to carry its own weight, while resisting the pull. Your balloon can always provide sufficient upforce. Being attached to earth, the centrifugal force of earth's rotation could even provide a lift of your tethered balloon further into space, enabling it to become even larger than 80km in size.
Actually.. When your technology is able to produce a a balloon, a tether cable light enough, long enough and strong enough, I don't expect any real limits on the balloon size itself, except for available resources: you'll have to fill a giant balloon with hydrogen or helium, which will not be a cheap enterprise !