Excellent thread!
Too many players confuse balance for differences in weight. I used to be that way myself until I bought a very precise scale and realized that some cues I thought to be different were the same in weight, but had about 1.5" of balance difference. Which is significant.
Which means that the cue's weight is perceived in a sense. At least for myself. How your hand/arm holds the cue and you "feel" the distribution of the weight and how your muscle memory compensates for that is what I'm trying to describe. When I am used to a particular cue, it almost feels neutral. That is, balanced in the sense that it doesn't feel heavy one way or the other. I can take the same weight cue with a different balance, and no matter what my stance or grip (choke up, or hold at the buttcap) - it feels either butt heavy or forward heavy. I have played with butt heavy cues and very forward heavy cues over the years and one big factor in getting used to a cue is when my stroke and feel for that cue is neutral in weight/balance distribution. That is, one factor in the transition period to a new cue is over with when it begins feeling neutral. Other factors are physical feel (taper, butt thickness, wraps) and playing characteristics like deflection level etc. I don't know about others, but in my case it seems my mind/body is always adjusting toward achieving a neutral feel, regardless of the balance. Exception would be cues that are toward the extreme ends of the balance point spectrum.
Right now my playing cue is exactly 38.5" balance point. Anything 37 - 38" feels too forward to me. Past 39" feels butt heavy. Of what I can get used to, to achieve a "neutral" feel is down to 37.5" and up to about 39"...in that range I can play with a cue and get used to the balance point so that it feels neutral to me. Beyond that range, the cue tends to always feels unbalanced. I'm sure I can eventually adapt, but it goes beyond the amount of time I'm willing to spend adapting. I get frustrated by the alien feel of the cue and give up. The last time I tried, I used a particular cue exclusively for a few months and still couldn't get 100% with it. Balance was out of the range of what I can get used to within a reasonable time. I went back to the previous cue and within a week I was 100% with it. I think the reason is that the weight distribution was causing my muscle memory to work outside of its realm. If that makes sense. Muscle memory takes time to develop and changes are difficult.
Balancing a cue can be tricky, since shafts can easily vary by a 1/4oz or more unless you select a matched pair or go custom.
I've also found that it is significantly easier and quicker to adjust to a new cue if it has the same balance point despite being a different weight. Weight matters no doubt about it. But balance point is more important, at least to me it is. With the same balance point, I can go up or down an ounce (which I consider a big change) and adjust pretty quickly. Balance takes a lot more time.
Just some thoughts. Some people probably think I'm crazy, but I'm happy I've found a way to quantify some of my preferences and understand what can work and what won't.