So what gauge would a balanced B be?
That depends on the gauges of the other strings. Most standard sets are not balanced and you could not make them balanced by changing the gauge of just the B string. Some folks argue that string gauges are selected to make the string to string tone even but I think that if that were true then standard set tensions would vary in some logical fashion. Here are some examples of standard sets from GHS. Not picking on GHS, in fact I use their strings a lot:
Bass Boomer Light G--33.6--35.2--35.9--36.1--31.3--B
Bass Boomer Med Light G--44.8--50.1--45.0--37.8--33.2--B
Bass Boomer Medium G--44.8--50.1--49.4--42.2--38.5--B
Pressure Wound Five G--43.3--48.3--47.2--48.0--34.0--B
As you can see some sets are fairly balanced, some are quite imbalanced. If tone were the driving factor then I would expect the tension to rise or fall monotonically from string to string, instead it varies almost randomly although the A and D strings are frequently the highest tension. I think that in truth the driving factor is how few string gauges can we manufacture while still offering string sets that will appeal to consumers? That minimizes costs.
I tune in fifths so I have to buy custom sets and I try to pick gauges that will give me around 40 pounds of tension for a 34 inch scale bass. String makers build too few different gauges of any type of string to allow you to do that exactly although Kalium comes closest, they do quite well in fact. Kalium does sell balanced tension sets so if you play rounds you can look at their string sets to see what balanced tension gauges look like. They make a vast array of them.
Link Removed It is a little confusing to use since it does not identify the octave the notes are in so you have to know a little about what gauges give your tension in what octave to use it. If you look at the chart then you can see that for a 34 inch scale:
Kalium Hybrid Gauges For 40 lbs Tension G--41--57--76--102--136--B
Actual Tensions For These Gauges G--38.5--40.36--40.19--40.35--39.25--B