Hoo boy. I remember every group I played with had different interpretations of how a combat round played. I believe your 'initiative' roll indicates the 'segment' of a round that your group starts at. So rolling a 5 on a d6 means your team starts at segment 5 of 10. From there you add your character's weapon speed or spell segment, and the total is when your attack 'goes off'. I think DEX bonus was subtracted from that but I can't recall if that was a house rule or not. So in other words, just because you beat the other group on initiative, they may very well go first because they have lighter weapons or faster spells prepared. You basically proceed segment to segement of a 10 segment round, resolving the attacks in order. It got complicated when slow actions went off in the next round! I don't think it allowed you to attack multiple times per round, except under certain conditions. Anyways, this system morphed into simpler 'initiative modifiers' in later editions. I may just be remembering whatever house-ruled interpretation that is stuck in my head, so take it for what it is worth.
Weapon length I think is used to determine who attacks first in a charge. Longer weapons go first, and I think that ignored initiative. Also, the lengths came into play if you were exploring tight spaces. I remember it often determined if the party order was single file, or 2 wide, or what have you.