Some great ideas evolving here.
I think having only a single bag slot, with a chance to increase to two as the character improves, is spot on.
I would go further, and not allow the larger weapons to be carried in bags at all since, in reality they couldn’t be.
Nothing to do with weight, as they weren’t particularly heavy anyway, just the size. Try fixing a weapon, that is almost as tall as you if not taller, to your body in any way that would be reasonably accessible in combat or even practical while travelling.
So brothers who want to wield the larger weapons, great-sword, billhook, spear would need to have them equipped from the outset. If they then wish to switch to something smaller in combat, then, abstractly they would stick those weapons in the ground or drop them, use the smaller item and then pick up the larger weapon afterwards.
Having large weapons in the backpack might not be entirely realistic, but it does add interesting choices to the tactical combat. Like keeping a guy with a billhook behind your front line, before having him switch to a sword and shield after the initial charge wears off. Or starting a mercenary with a spear and shield to withstand the first wave of orcs and then switching to a greatsword once the lines have been established.
Having to drop the weapon, arm the mercenary and then go back for it if you want to use it again also bogs down gameplay and just makes it a hassle to use. Making it a hassle to use makes the player less likely to utilise it, which shouldn’t be necessary as it’s not a heavily unbalanced tactic. Items conveying a fatigue penalty is probably enough to dissuade players from hauling around unneccesary items. I kind of like the idea mentioned earlier of making those slots more valuable by giving them less, which also makes the extra slots perk more interesting, though you’d keep the problem of switching between a two-handed and one-handed + shield set.