Creamium explained it briefly but the other thing you want to pay attention to is the ParamBonus section. Each weapon can get a damage boost from 4 of your stats (strength, dexterity, intelligence and faith). The scaling goes from E to S where S is best so if you want to get more damage from a weapon you like, boost the stat that benefits most from scaling. Your Hand Axe scales to C with strength and D with dexterity so you'll get more of a bonus by increasing your strength with that weapon
Try a few different weapons and see what you like the feel of then upgrade one to +5 with Andre and you should be set for the next few sections of the game. Weapons that require higher strength to wield tend to be slower and dexterity based weapons are usually faster
Some weapons also have additional effects seen in the Aux Effects section. Some of the DEX weapons for example inflict bleed damage. If you land a few hits (even if they're blocked) the enemy loses a big chunk of health and satisfyingly squirts blood everywhere
Finally, you can reduce the strength you need to try a weapon by wielding it with 2 hands. This increases your strength by x1.5 - so with only 16 STR, you can 2-hand a Zwiehander (which usually requires 24 STR). You can use this to try out some of the weapons you already have but don't have enough strength to swing normally
