No, because the weight given for the BT one isn't just the gun itself, it's the gun, the mounting, ammunition feed, the motors that allow it to traverse and actually aim, etc. Everything that needs to be installed to make that weapon actually work as part of the overall mech, which will add a lot of extra weight.
No, I actually did account for that in a lot of my musings, because this isn't my first 'why do BT ballistics suck so much' rodeo.
That's one of the reasons why I specified WWII MGs, AC/2s, and maybe AC/5s. Because I've actually looked them up, and they manage to fit more guns per ton up past the AC/2 range, but it pretty rapidly gets much heavier in WWII technology.
But since you brought up MGs, the turret on a HMMWV weighs 200 pounds. That includes the controls, the big ass ring gear for spinning around, and a bunch of armor that wouldn't be on the 'MG weight' in BT since the armor would be part of mech's but we need to change up the format of the control to smaller gears and give it at least a 90 degree cone from it's hardpoint. Probably fair to say that it weighs about the same at that point swapping armor for a more complex control system gun-side and gun side ammo feed. ~285 pounds with a mounted Ma Deuce. That's .1425 tons. Less than a Clan weapon for a .50 cal machine gun. It even has 200+ pounds to play with to even weigh the same, for basically the same weapon that is described in BT. 12mm or .50cal. Also it's something that's still used and effective in BT as the M2 is actually listed somewhere.
Bofors 40mm L/60 (The WWII to 1990s weapon that would fit the profile of an AC/2 as far as I can tell. Though the Oerlikon 20mm might be the AC/2 and the Bofors the AC/5 bracket. It has been a hot minute since I last spent hours doing this research for fun) has a carriage weight (it and it's mount) of 1,151 lbs, or a little over half a ton. Normally has a crew to operate it. But just to reach the six tons of a BT AC/2 it has ~5.5 tons of control motors systems and ammunition feed.
The weight, in WWII tech, starts to rapidly get heavier than the BT counterpart. Given that the best information I can find on an Abrams places it's entire turret (cannon, controls, specialist systems, electronics, mounts,
armor etc) is that it weighs
27 tons. And that's a 105mm (or about the /5 to /10 range) cannon. Without knowing how much of that can be stripped away, I can't lock in anything for that.
In the low caliber end, modern tech is
absolutely better than BT tech, worse case we'd need to actually start building autocannons and HE rounds again. In the interim, I think I'm right to believe our missile tech makes Clanner missile tech look like noobsauce.
I think we have superior high caliber end cannon tech in terms of
power, and effectiveness, but
not weight.