So as the question is asking what is everyone's opinion on the best light-weight weapons.

I'm looking for the most powerful, useful, and interesting weapons that can be used in the game while making it easier to carry more random crap. This is also partially because I'm having trouble deciding what weapons to bring into the HH dlc (ps3 so no dlc yet).

categories include: guns, energy weapons, explosives, unarmed, and melee.

I'm not much of an energy weapons user yet (working on it but have no idea what a good light-weight weapon might be for it. same goes for melee, unarmed, explosive
My light-weight weapon of choice is Lucky (unless I specialize in one of the other fighting styles).

Lucky is considered a hold-out weapon and is much more useful than say the 22. It requires a sneak skill of 50 but if you decide to go in sneak at all then this is extremely useful.
it only requires a strength of 3 to use so able for anyone to use. with implants and perks.
weight is only 2.5
the item hp is 225 and is able to be easily repaired with .357 (relatively easy to buy/find).
95 percent chance of critical.
dps: 82 right off the bat with a possibility of getting to 131 with perks.
has a dmg of 30 with a possibility for 9.9 more with the perks.

needless to say this is one of my favorite weapons and considering its weight it is very easy to carry. I have almost all of my characters carry this gun with them. not to mention it looks cool.

EW's are out tbh, they tend to be heavier and their ammo is definitely heavier in bulk.
9mm, 9mm smg, then 10mm, 10mm smg, .357 for grunt work, varmit rifle then sniper if needed for range work.
Caravan shotgun tbh early on with no other option in shotguns is very light, very fast and has excellent perks.

Later on the marksman carabine should be enough for most situations.

All this though is personal opinion.

Im quite fond of the Maria and A light of the Darkness and for melee/ unarmed chances knife and love and hate

I think its always nice to have a light weapons to use for weaker enemies to conserve item hp and ammo for more powerful weps and for when you feel like you need more challenge

If you want a powerful lightweight weapon may I suggest the ranger seqouia. You can get it after completing the ncr quest return to sender after Hanlon commits suicide search his body for it. Though you could just kill him if you are against the ncr.

Lucky
Chance's Knife
Gobi Campaign Sniper Rifle
All the ass-kicking you need done at all ranges for less than 10 pounds.

Veterens of ncr may or may not also carry it later on in game or at higher pc level

The weapon I have in my inventory atm are:
Fully modded 10mil for sneak attacks
Grenade rifle for the damn deathclaws (no wild wasteland this playthrough & the unique gauss was broke when I got it)
Hunting Rifle
Lucky (I use this the most even on deathclaws on occasion though this tends to get me killed)
Plasma Rifle
Shovel (for grave robbin')
Sniper Rifle
That gun

At this point that is what I got. though most of them are unnecessary. Don't quite remember what I had towards the end on my first playthrough but I know I always use Lucky as Colt SAAs make me all gitty on the inside.
To answer your question, however, the 10mil submachine gun is a solid choice.

Light in shining darkness,Lucy, Weathered 10mm pistol,maria, and mysterious magnum.

A Light Shining in Darkness (That's the only pistol and light weapon I use)
Marksman Carbine (Useful in most situations) (Good assault weapon) (Gun gets boring to use when you use it too much)
Brush Gun (Good for taking out extremely tough enemies, or if you're just bored of the Marksman Carbine)
That's pretty much my loadout. I'm not really a fan of lightweight weapons.

For light gun I'll vote for the Hunting Revolver. Handy scope, and packs plenty of punch. I've not gotten a seqouia since it generally doesn't show up til high level, and I usually stay on good terms with the NCR. The Seqouia is a very rare variant of the Hunting Revolver.

For energy weapons, the Recharger Pistol is a good choice. It isn't the most powerful energy weapon, but still packs a healthy punch and there's no bulky ammo to carry around. Pew Pew is supposedly a powerful weapon, but reportedly blows through ammo very quickly. The Plasma Defender is a pretty powerful energy pistol, too.

im gonna have to go with mysterious magnum.just started using for 1st time and im lovin that it plays the guitar twang every time you get it out.

If you have the Honest Hearts expansion then A Light Shining In the Darkness. At 100 Guns skill and (admittedly with a high crit build and the Grunt Perk) I've been using it to hunt regular Deathclaws (I'd already killed all the double health Deathclaws at the Quarry so I can't say how it would work on them).

Without the expansion the Lever Action Shotgun can be pretty good as well but you need to invest in several perks like the Shogun Surgeon for it to really shine. A fully modded Cowboy Repeater is also pretty light and, with the Cowboy perk does decent damage against low armor targets.

If you want to run with only one gun ammo can become an issue so Love and Hate or any regular set of Spiked Knuckles are good for fly swatting low level critters as is Chance's Knife.

Pushy...or if you don't mind it being fragile...Ballistic Fist.

Once you get Strong Back and Pack Rat, weight largely ceases to be an issue.

However, if you must be picky, I'd suggest the following weapons, all of them with weight of 5 or less:


Guns:

Gobi Campaign Scout Rifle
Riot Shotgun
12.7mm SMG
Brush Gun
Trail Carbine
Ranger Sequoia
Hunting Revolver
Mysterious Magnum
10mm SMG, fully modded (surprisingly lethal on anything with low DT).
Ratslayer (even if you're very high level, it is still useful for picking off weak enemies with cheap ammo).
Lever-Action Shotgun (if using Shotgun Surgeon and Cowboy perks, that little weapon has a pretty good punch).


Energy:
Plasma Defender (weight of only 2!)
Pew Pew (massive ammo consumption is somewhat mitigated by the absurdly high DAM; you don't need to repeat your shots too often).

I stay on the NCR's good side as well. But that doesn't stop me stealing the sequoia from Chief Hanlon. Also you don't need to be a high level either, you simply need to go to Camp golf.

Last time I dealt with Hanlon he bugged out and wouldn't kill himself when I tried to turn him in. I didn't want to take a chance by pickpocketing him either, though I suppose I could try if I was dying to have the sequoia.

12.7 pistol w/silencer is still a fave if I need close-up silence.
With HH, agreed about A Light Shining in Darkness. It is also a holdout and beats Lucky, imo. But then, I don't like revolvers much in this game so..
RatSlayer is a good choice & still useful later, especially with AP rounds.
Pushy.
Love & Hate.