Some thoughts on what could be causing the big armor, tiny weapon problem.

1. Alt Jobs that share gear. I play BLM, PLD, and SCH. That means at any time, I could toss my i130 armor on my SMN and have a huge ilvl, despite the best weapon I have being the Titan book. Somehow never got around to picking up the Diamond one off Shiva. (I personally consider any weapon above i110 to be "good enough" for all current content)

2. Poor logic/understanding of stat weights. A player earns, say, 1500 poetics, and looks through the list o' stuff you can buy. They see 1300 and a tomestone for a 120 weapon. Or 850(ish) and a twine for a 130 chest, with enough left over to buy and ring, and nearly there on bracelet. Most players will choose to upgrade 3 slots over 1, thinking it will provide a greater bonus.

3. Deliberately screwing with ilvl to get into content. This is the one that pisses me off. The other day I joined a Shiva EX farm party for a pony, and for some reason, the tank just kept dropping. I checked the tanks gear. Solid for Shiva. WHM? Looked good. SCH? WTF. i55 Grand Company Book. Guy was there for the Shiva book, and hadn't bothered to run HM primals, hit the markets, or burn through relic to Zenith, even. When you can buy an i70 book on the MB for 200k gil, bringing anything lower to an EX primal farm is just saying "I don't care, carry me"