You could try Recount, but honestly you're not going to find much in the way of a lightweight damage meter. Damage meters of any variety log a crap load of information. You could reset the meters after each attempt and that'll keep memory low, but overall they're not designed to be low memory addons.
Another possible solution is to use WWS.
Wow Web Stats Get an addon like LoggerHead to automate turning your combat log on, or just use /combatlog to save all the data. I prefer using this to any in game damage meter to be honest because it's much more informational than any damage meter.