Its an old unintended mechanism. It used to be the case that you actually had an invisible buffer up to 135. This was evident because people were firing all weapons and the weapon power was never dropping below 125. This was fixed some time ago, just before F2P I think. It now seems to have been un-fixed. I got a couple of people in the pvp forum confirming it too.
It sounds to me like there are two potential explanations.
ashenfox and OP discussing a possible bug:
-- shifting your power doesn't have anything to do with altering your consoles or loadouts, so we can more or less ignore those factors
-- assuming weapon energy drains and recharges are constant, increasing your weapon energy above what gets you 123-125 should result in excess energy being wasted/unnecessary
----- thus if you fire a weapon, hit for X, slide power up, fire the same weapon and hit for X+Y, I agree it suggests something is going on here that we've been told shouldn't (barring any debuff effects or the like from the first firing)
The other possible case is that weapon power levels have an effect on weapon drain and recharge rates. I wouldn't be surprised if people immediately shot this idea down with facts from patch notes or whatever, but I have been suspecting while reading that higher settings direct more of your ships efforts, so to say, to keeping the energy recharged. If that is at all true, pushing as close to or "above" (though not really) to 125 would help keep weapons active from dipping you as low as normal, making for more consistent, higher damage.
-- 125 is still a cap
-- the overall DPS increase would be due to keeping weapon energy high more often
This latter theory could fall to pieces, though, if you consider just firing once for testing, pausing for a full recharge, and firing again. Maybe EptW, for example, can keep the discharge from a beam array going off from dipping the energy as low and thus the higher damage that seems to be 125+, but also maybe I am grasping for straws for an explanation for the issue.
A means to parse and record combat log data could be helpful.
I have to agree in regards to power recharge
Setting to near the cap does provide significant recharge to weapons
I did a test by reducing my weapons power level to around 100 and then fired
I notice a significant drop in power levels compared to when set around 123
Therefore the only advantage to set near to cap is greater power recovery, which then means more actual dps for longer duration
To note I am new to this within this mmo, but curretly running tac builds with :
Fed: duel hvys x 3 single quantum torp, turrets rear using a vector
Klingon: quad cannon, 2 duel hvy ,single quantum torp front, turrets rear on guramba siege destroyer
To note not sure if buffs and debuffs are hitting the cap or cause it to go over
Test were run in alpha stike and non alpha striking modes
Obviously the drop in power more with alpha strikes but the recovery was very noticable
Soft cap is 125. The mystery cap is 135. This has been observed by most escort pilots with wep at 125/100 and EPS flow regulator skill maxed with consoles. As a result they will rarely see a significant power drain using cannon weapons due to the cool down between fireing cycles. Effectivly boosting burst and sustained DPS.