Standard level progression is that your first weapon is weak, non-ranged, etc. and then you pick up more powerful weapons as you go. So why is it that often well into the game you get another chance, long after it’s pointless, to get another of that weak weapon? Now I understand that part of the fun is starting at an advanced level and seeing if you can survive with just the assets you can pick up in that level. The problem is that they never give you the weak weapon at the start of that level. In other words, if I’ve somehow managed to survive starting with my bare fists in a level full of submachinegun-wielding killers, wtf is the point of offering me a baseball bat AFTER I’ve gotten past them?
Example, please?
Not a great example, but in Civilisation you can get Pikemen after Musketeers become available. However, they do get bonuses that musketeers don’t have available.
I think most 3d shooters or rpgs should walk a fine line between allowing access to better weapons in an escalating progression, but also giving some freedom for people to progress as they like, and to give the appearance of randomness in the distribution of weapons (which is satisfying for a player’ emersion into the game world). If the game provided the exact weapon I needed/wanted right before the appropriate battle, every time, I would be sorely dissapointed.
Oblivion did it poorly, Fallout 3 did it well.
There’s also the possibility that the weaker weapon is just plain fun. Thinking back to the game Serious Sam, there are plenty of weapons stronger than the chainsaw, but I’d still run around with that thing for hours.
Ok, I was replaying Half-Life: Opposing Force yesterday, which is what prompted this. On one map (of2a6), if you’ve continued play from previous maps you already have weapons. If you’re starting new in the level, if you can get past six heavily armed assassins to reach a guardroom, you can get a combat knife.
Maybe it’s meant as ironic. If John Rambo did more with a combat knife…
Could it be a way to handle difficulty levels? Play a map on easy and you see the BFG 9000, combat knife and 9mm, play it on medium and see the Knife and 9mm, play it on ultimate and only see the knife?
I don’t remember that part of the game but, if I’m not mistaking, you get all your weapons taken away at some point and have to reacquire them again.
I’ve noticed what the OP is talking about before (not just with weapons but all sorts of powerups that come too late), and always figured this was the reason for it.
This actually worked really well in Serious Sam. The game trained you very quickly to view any powerups with a mixture of satisfaction and fear, and the stronger the powerup, the more so. Seeing a massive superweapon and all the ammo you could want for it, just sitting there in the middle of a vast, empty plaza…yeah, it’s all about to hit the fan.
Then again, immersion very much wasn’t that game’s intention 
Yeah that was a fun game. I mainly remember the final? battle - facing down zillions of buffalo-like creatures with a canon. But as you say, immersion wasn’t the point. 
In the very underrated Command and Conquer Renegade the opposite happens. You end up losing your stock rifle when you get thrown in jail and you never get it back. From that point in the game forward there is exactly one guy carrying that weapon and half the time he does not drop it when you shoot him. So your “least powerful” pickup weapon (since you always have a pistol) becomes a chaingun. This is probably because the enemies you face at this point in the game aren’t too impressed by precision three-round bursts, even those aimed at faces. But I miss that gun.
That’s what happens in Goldeneye - after the first Severnaya mission you have to escape from the brig-thing, and afterward you pick up an automatic rifle with minimal ammo and some throwing knives. You don’t really want to use to rifle because it brings then entire garrison running, so you have to use the crappy throwing knives until you can bust into a safe and get your silenced PPK (I think the game calls it a PP7) back.
Bring on the garrison. They drop enough ammo to kill them all…until you hit the alarm button again and bring more.