What I did:
I took out my Master Rules and Solaris VII Rules and made a spreadsheet with all the numbers given in those books.

Now these are a lot of numbers and you can't see much. So I decided to condense all those numbers to a more manageable format. First I removed the Min, Short and Medium Range columns as I figured what the heck I don't need those I want to know how far I can shoot and those increments are useless in MW Games anyway (Why should it be more difficult to hit someone with a small laser then with a large laser at 90 meters?). Secondly I condensed the Damage and Recycle columns to into one DpS column. Then I figured I reduce the Heat, Critical and Tonnage columns into one Construction Points (CPs) column. One Critical equals one CP, one Ton equals one CP and one Heat equals two CPs (because 1 HeatSink would cost 1 Critical and one Ton). I left Ammo alone for now.

Now I tried to come up with a solution to incorporate Ammo into those neat CPs. What I did was I calculated the amount of Ammo needed for 1 Minute of sustained fire. Of course this meant that I had a lot of fractional numbers, which is impossible according to the rules but I had to balance it out somehow. Now I doubled those results (because Ammo also needs one Critical and one Ton) and added my CPs. Now I took these 3 Values and played around with them for a bit and I came up with Range * DpS / CPs and called it effectiveness. And I have to say I am quite happy with the result because it made some sense (at least to me).

Now let's have a look at those numbers :
Energy Weapons :
As you can see nearly all energy weapons have an effectiveness of about .5 to .7 with the exception of the medium laser which pokes out quite a bit (if you would increase its cycle time to 7.5 it would still be top of the class but not by that much .... maybe an error?), the flamer (who cares about flamers?) and the pulse lasers. BUT if you remember that those pulse lasers are supposed to hit better than the rest of them that would make kind of sense (wouldn't it?). Considering that energy weapons have no ammo and therefore would last indefinitely and there is nothing to go boom and that they have no travel time, I think that it would make them nonetheless quite effective and you would have to increase that number (keep in mind the heat drawback of energy weapons is already incorporated into the CPs and there are not really any other drawbacks to energy weapons) . There are more pros and cons but those are more taste then actually something that you could incorporate into a formula (I don't argue about taste ..... it's pointless).
Ballistic Weapons :
Now I have to make some assumptions on these considering how they will work in the game (no one knows exactly how they will work). First of they seem to be quite effective (and somewhat all over the place). AC/5s and AC/10s seem to be equally effective, AC/2s way above average and AC/20s are not effective at all. (first) BUT if you consider that AC/2s have a very long Range and that you would seldom be able to take advantage of that range I think they are not quite that effective (I go into range and terrain later). (second) BUT if you consider that the AC/20 is one of two weapons in the game (as of now)that is actually able to take of heads and/or limbs with one shot then this would make it a whole lot more effective in my eyes (is this considered taste?). Now we come to the assumptions part. At first glance the Gauss Rifle is highly effective. BUT a "normal" cannon (read AC) should have a very high muzzle velocity and therefore a rather short travel time (about 3000-4000 meters per second) and a Gauss "ball" travels roughly at speed of sound (about 333 meters per second) which means a rather long travel time (2 seconds to reach its max range) making it rather difficult to aim at fast moving targets in the distance thus reducing its effective effectiveness (whoa, is that kind of sentence constructions really possible?). Given that all Ballistic Weapons have travel time, Ammunition (limited) and a chance to explode it should lower their overall effectiveness quite a bit. The LB-X ACs have the additional drawback of not hitting with everything they have and scattering their damage all over though they are easier to hit with. Ultra ACs can Jam ...nough said.
Missile Weapons :
All LRMs have roughly the same very high effectiveness, considering though the very slow travel time, Ammo needs(read limited # of salvos and chance to go boom), lock-on requirements, countermeasures available, large minimum range and that not all missiles will hit, this would have to be reduced a lot. SRMs have a lower effectiveness then LRMs and I would say it's quite ok considering that they have nearly (no lock-on, no min range) the same drawbacks as their long range counterparts. The SRM2 drops out a bit because somehow they only carry 90 missiles and all others carry 100 and the Streaks reduce the cons by one (all missiles hit).
Range and Terrain :
Now all these numbers are for open terrain and clear line of sight. If you would instead reduce the maximum range of all weapons (that have more than 13 hexes) to 13 hexes (400 meters) which would roughly equal 1-2 city blocks, we have a completely different story. Energy Weapons, SRMs, Gauss, and AC/20s would really dominate those maps with no equals in sight, which after all is no big wonder.

Conclusions :
Yes I know it's not perfect but it can give you some pointers whether one weapon is better than another or how Overpowered (medium laser?) or Underpowered a weapon really is.
PS.: The weapons in gray are not available until the end of the 2050s
PPS.: Wow thats one big post ..... sorry :/