Weight is a weaker condition, since you can construct a polynomial weight sequence that results in linear height.
In general, height is the easiest thing to restrict, but doing so restricts dynamic performance optimizations - you can't use splay trees, for instance
> Weight is a weaker condition, since you can construct a polynomial weight sequence that results in linear height.
I'd like to hear more. The varieties of weight-balanced trees I'm aware of all have logarithmic height.
> In general, height is the easiest thing to restrict, but doing so restricts dynamic performance optimizations - you can't use splay trees, for instance
Good point.
BTW, you might be interested in Bose et al.'s "De-amortizing Binary Search Trees" <https://arxiv.org/pdf/1111.1665.pdf>, shows how to keep height logarithmic with "essentially any Binary Search Tree" (their phrase).
In general, height is the easiest thing to restrict, but doing so restricts dynamic performance optimizations - you can't use splay trees, for instance