English has a big problem - it uses the same word to mean multiple things. So it is with English weaving terminology which sometimes makes it difficult to understand. That is where context comes in.
So, the word balanced in weaving.
We use the word to describe a textile that has the same number of ppi and epi, given the same yarn is being used in warp and weft.
But the other meaning typically refers to how the design looks in the cloth.
Balancing a weave structure means understanding how the weave structure works; in other words, how to make borders, side to side, top to bottom. The motif should be 'complete' not cut off part way through.
Typically weave structures like overshot, lace weaves, Summer and Winter, and on and on are routinely 'balanced'. Twills can be balanced as well although not always.
When it comes to twills, balanced does not mean that the twill line begins and ends on the same shaft. If that is the case, one of the outside ends will not weave in and will have to be treated as a floating selvedge, or simply left off. With twill you want the twill line to begin on an even shaft and end on an odd, or vice versa.
In the draft above I have taken the sequence we call Wall of Troy and added straight draw to each selvedge, then in the treadling. The straight draw frames the Wall of Troy and makes the cloth look 'complete'.
I also like to 'frame' the design to keep the focal point in the middle of the cloth and adding such a frame helps to do this.