My experience with BB is limited to Metoprolol and I have moved up and down in dose levels and the only affect I clearly see/feel is a change in my HR. Seems there is a non-zero BB level for me if I am to keep resting HR below 90. For me that is a pretty stiff dose, 50 mg once a day.
I have never felt any stiffness, well none I don't ascribe to age...it could be related to BB dose changes, but I don't think so.
I do understand that abrupt changes in BB dose levels is not recommended.