They should do the same damage unless you have a high crit rate. If you are getting varied consecutive hit numbers there might be something else going on.
Ok, so I figured I had some spare time to at least test whether Surge increases overloads damage and it does not appear to.
With a weapon damage of 117, normal light attacks did 85 damage. Heavy attacks did 209.
With surge increasing my weapon damage to 163 (due to pvp 5% boost), light attacks do 112 damage and heavy 273.
Overload did 207 damage with light attacks and 266 damage with heavy attacks with and without surge activated.
This leads me to think that whatever overload adds 9% damage to it isn't weapon damage or weapon attacks. I couldn't find a 9% increase in any of my figures and fighting unarmed (weapon damage 0) didn't change anything.
This likely means that Bound Armaments will have no effect on Overload either as it seems to base its damage off something non-weapon related. Just goes to show the importance of testing.