Gantinite has no weak points, aside from one critical flaw. The helm has no visor. It covers the forehead and mouth, but your nose and eyes are vulnerable. Naturally blades and hammers and maces can still crack the armour given a few solid, repeated strikes from knight-class weapons.
Don't worry about exhaustion or weight limits too much. The only reason you're tired is because the fight at Hiketo lasted a month and you haven't slept since it began (still working on that prologue thing). You can carry quite a few weapons on your person really. Besides, you can always hire a few patsies to carry your things or take on a squire at the chapel. But don't worry about that now, we'll get you an entourage soon enough.
Let me scrape together a list of weapons for you guys real quick. I'll probably edit this to answer some of the other questions you had.
The honest-faced knight is no merchant, and immediately launches into a loving rant about his stock:
Of course I have shields, mostly tower and kite, but there a buckler or two hereabouts, and I've got hundreds of blades, including a few good two-handers. No short swords though, except mine, and thats not for sale. Rather disappointing that I haven't fought more warriors with short blades, seems that every fledgeling knight out there these days wants something impressive. I need to kill more Litelachians. They don't even know what longswords are.
Anyhow, there are a couple halberds at the front here, but they're quite good and I'm rather fond of them. It'd take a pretty penny, but I would be willing to part with one, and I'm sure you'd be intensely pleased with whatever choice you make. I've got one or two spears and a dozen of those Kiltran clack-lances. Nasty weapons those.
I've only one repeating crossbow that works. Its not fancy, but its got arms made of softened iron, built for siege work, and its served me well on occasions where I've had need of it. No real bows I'm afraid, but its not hard at all to find those in other parts of the village.
These here I'm particularly proud of. Red and blue Striker Morningstars from Tachjlankt. Anything you hit freezes instantly, or bursts into flame, depending on the colour of course. I already know you haven't the money for these. I've got some good maces though, as well as a pair just as long as a bloody stave. Those ones I took straight from the hands of a pair of Patrichlan knights. I had taken a pearl necklace from a sunken ruin, and it must've been one of their ancient temples. My ribs still hurt from that fight, took me half a day just to kill one of them it did, and two more just to have the other slip and fall from the bluff we were fighting on. I climbed all the way down the cliff with seven broken ribs and a shattered hand just to get his weapon. Its just as beautiful as the day I earned it.