The two most important aspects will be:
1. Reach: Being able to hit your opponent at longer range is always huge advantage. That's why most soldiers used spears, pikes, lances and other polearms as primary weapons. Swords were almost always secondary weapons for use if the primary weapon was lost or the fight became too close for the long polearm. Of course, ranged weapons have even longer range, but lower accuracy and limited ammunition.
2. Weight: The effort required for sustaining flight, and for all manoeuvres, is directly proportional to your weight. Also, swinging anything heavy around would get you out of balance quickly as you don't have any solid support.
So what weapons come in consideration:
* Bows: I am going to suggest bows rather than crossbows mentioned in the other answers due to their lower weight. Crossbows were mainly preferred as they required less training, but in trained hands a recurve composite bow is every bit as deadly.
* Bolas: Shorter range than bows, but more likely to hit both due to their larger size and because you are targeting the wings with them—the wings are not all that vulnerable to arrows since most of their area is just feathers and piercing through them won't cause pain and very little damage. On the other hand bola will interfere with moving the wings, which is crippling.
* Blowguns, for the low weight of their ammo, especially if you dare to dip it in a poison.
* Lasso: Similar to the bolas. You'd probably have to let go of it if you score a hit and let it plummet to the ground with the opponent, but at least you'd get to keep it if you miss. The price is the limited range.
* Lance: A long, rather thin (for low weight), spear would be most practical melee weapon. Attack would almost always involve flying with it outstretched forward and using your own momentum to impale the opponent from behind or other angle except head on (which would usually end in mutual kill) in a style rather similar to cavalry charge except with no shield you'd rely more on manoeuvring advantage.
It should be long enough to reach beyond your wingtips so you can use it to deflect opponent's spears and also bolas and lassos.
* <PERSON>: Adding a blade to the tip might be useful because as the wings are not that vulnerable to piercing attacks they are much more vulnerable to slashing ones (as that has higher chance of hitting the ‘arm’). However, the blade would make it heavier and swinging it around would make you turn the other way, which would be hard to compensate without the luxury of fixed support one has on the ground. 358
Might be a thing for the strongest elite fighters.
* Spear: A shorter spear as side-arm for ranged fighters so they don't feel completely helpless when they are out of ammunition. Not much actual value though.
In either case:
* Shields are not practical as they are heavy, cause a lot of drag and can't protect the outer wings anyway. So you'd need to rely on manoeuvring for defense.
* Since you are very vulnerable from behind, you should be flying with wingmen to cover your back. Flights of 3 or 4 may be an option.
* You need certain speed to fly efficiently (there is a speed with minimum drag; flying slower produces more drag and thus takes more effort to sustain) and manoeuvre well (at lower speed your wings can't generate as much lift and you need that for accelerating sideways to turn). You are rather large for flying creatures, so the practical speed would be quite high. Say about at least 30 knots (55 km/h).
That's pretty fast. Faster than horses. At that speed, there can't be much parrying. The fight will be series of charges and evasive manoeuvres. However flight will be usually quite smooth (subject to weather), so aiming the bows is not as hard as from horseback.
* Most of the time you'll have critical shortage of cover. However, sometimes clouds will be usable and surprise take-offs from under cover may be an option.
But don't underestimate the dangers of flying through clouds—while being able to feel the wind around your wings does give you some advantage over aircraft pilots, you are far from immune from spatial disorientation.
Also, many encounters will be fights for some resource and that will obviously be on the ground, whether it is a city, fortress, mine, factory, etc.:
* You'll have some ground-based artillery, shooting from larger ballistas. Instead of big bolts, they are likely to shoot nets or some variants of bolas.
* You still get to do bombardment, with various things. Flechettes may be effective against personnel, but to take out the defense weapons, fire will most likely come in handy. 160