Yes and Yes ...
Balance, most assurdedly, affects how heavy a cue feels. I have felt 19's that felt like a 21, and vica versa. I prefer a heavier cue, always have, and shot with a 21 over 30 years until I got my first custom, then I went with 20.2 oz. with forward balancing (19" centerpoint), 12.75 mm Layered Hercules tip.
My break/jump cue is 19.5 oz with 14 mm phenolic tip