How do I equally balance tmux(1) split panes?

Vertically

select-layout even-vertical
Usually assigned to: Ctrl+b, Alt+2

Horizontally

select-layout even-horizontal
Usually assigned to: Ctrl+b, Alt+1

You can use ctrl-b space to cycle through layouts with even spacing, but that won't necessarily preserve the layout you had.

From the command line you can use

tmux select-layout tiled

to make your splits all roughly equal size. You can bind that to a key command as well.