I know that heavier 'mechs generally do more melee damage, this is well documented in the game.
However, I swear that my Orion does more damage with it's AC/10 than an Urbanmech or a Centurion when I'm using Breaching Shot despite the numbers shown on screen not reflecting it.
Similarly I seem to kill things quicker with a Grasshopper firing 6 medium lasers + 1 large than with a Hunchback firing 8ML, despite the fact that the Hunchback should be doing more damage with the 3 extra lasers (25*8=200 vs 6*25 + 40=190).
Not to mention I often refit the Grasshopper drop the large laser for another medium (and often drop the LRM5 or swap it for an SRM2) and equip flamers with the weight saved to overheat enemy 'mechs.
I still seem to kill faster with the Grasshopper.

Also the Cataphract 0X seems more effective than the Trebuchet at range despite both using an AC/5 and a PPC.

Am I just imagining things or do heavies have a subtle advantage in addition to more armor?

the mech doesn't effect damage ... assuming the shot hits

What you might be seeing is the factor that arm mounted weapons have greater accuracy. That means on average if you fire 20 shots with weapons mounted on arms vs torso mounted weapons you will hit 1 more shot.