Check the Mercantile houses (market wards) for weapons. Some really low (like 1v 1-15) weapons may be cheaper from the vendors but other ones will be cheaper from the wards -- or as people have mentioned, look up the mats on lodestone or mooglebox.com and see if you can find a crafter^^

Levequests, sidequests (You'll notice a "!" on the map and above an NPC's head when they have a quest for you, more open up as you level), and main scenario quests net a nice amount of gil. If you do quests in all 3 cities you will acquire a fair amount of gear too so you can save money there.

You can make a nice amount of gil levelling up a DoL job -- fishing is pretty cheap and is a nice moneymaker, alchemists and culinarians will buy your fish from the mercantile houses.

Miner is nice if you want to sell ores to Goldsmiths, Blacksmiths and Armorers

Botanist is nice if you want random mats for Culinarian, Carpenter and Weaver etc.

You can even make nice cash from killing animals for their skins, such as sheep, goats etc. NPCing marmot skins nets around 500g each

Remember while you're levelling -- some gear upgrades you can skip, if you can hold out an extra 2-3 levels while you're in the pre-40 stage and make sure your next upgrade is a significant bonus you'll save a lot of money since you'll level out of gear/weapons quickly.

Sorry for rambling, I hope this helps♪