thanks for detailed explanation.
But what is the purpose to use pistol (balistic, laser, plasma) if you have rifle of the same type ? And often heavy version is too bulky leaving more or less half of weapons that actually matters.
For aliens it is defined in list of item levels but for human player ?
Well, I do it for...I guess role-playing purposes. It's perfectly possible to carry a rifle or something in your bags as well as whatever you have in-hand, as long as you have the strength for it. Sure, there is probably one 'uber' weapon per tier that all your guys should be using at all times, but people like to vary it up a bit. And some people like using 'heavies' - rocket launchers, that sort of thing.
All your guys have strength. Carrying more stuff will increase said strength. Eventually your guys will be the equivalent to the Hulk and can carry freaking EVERYTHING. It's just a matter of getting them there. Some guys start with insanely low STR, so it's more efficient to stick them to pistols. Pistols don't way much, take fewer time units to fire. So you can get in closer (if you go over your STR in weight, it starts to eat up your time units, so your guys have fewer to use...or maybe it's energy, either way, they get tired and aren't efficient) and then have a better chance to hit since you're closer. If you stuck a rifle on someone with low STR, there's a good chance it'll cap out or go over the STR, and that causes problems. So start the weak guys out on pistols, upgrade them to rifles when you can, and just work your way up and around like that.
The plus side to pistols is (and I'm not sure how this works in OpenXcom) you CAN carry something in your off-hand without a penalty. Obviously functions that way in real life, too. So you could make, say, a medic that carries a medkit in one hand, and pistol in the other, rather than having to fumble around with rifles and such.
Really, it's all about how YOU want to play. There really is no RIGHT or WRONG way to gear your guys. Although obviously pistols do less damage, heavier weapons do more, but there are other balance issues (aiming penalties, more or less time units to fire, etc) for and against each weapon type, you just have to figure out which you like the best.
Me personally, I'm using the Final Mod Pack, and each tier, I stick my guys with Sniper Rifles. Takes a ridiculous amount of TUs to fire, I can't move very much each turn, but they're accurate and they do a hefty amount of damage. I also have guys who carry stun weapons exclusively. Tazers are the start, then dart guns, then stun bomb launchers. That's how all of my crew are. Most snipers, the rest stunners. I don't use explosives or heavies.