Polar Star
The first weapon you find. It can be traded in for different weapons depending on who you give it to.
Level 1: 1 damage, 10 xp to level up.
Level 2: 2 damage, 20 xp to level up.
Level 3: 4 damage, 10 xp to MAX. Only 2 shots on screen at once permitted.
Machine Gun
By trading the Polar Star in to Curly Brace, you can acquire this vulcan cannon. It is relatively powerful, shoots long range rapid shots and at full power can be used as a means of propulsion.
Level 1: 2 damage, 30 xp to level up. Ammo regenerates slowly.
Level 2: 4 damage, 40 xp to level up. Ammo regenerates more quickly (5 per second) and spread fire.
Level 3: 6 damage, 10 xp to MAX. Ammo regenerates similar to level 2, hover/fly when shooting down. It is possible to float indefinitely.
By trading in the Polar Star and Fireball in to Chaba, the weapons dealer in the labyrinth you can acquire this weapon. It acts like a long distance fireball that can is useful since it can shoot through walls.
Level 1: 4 damage, 30 xp to level up. As many shots as you can shoot, fires through walls!
Level 2: 6 damage , 40 xp to level up. Moves like snake (think Wave Beam in Metroid), goes through walls.
Level 3: 8 damage, 16 xp to level up. Longer range, still goes through walls. 4 shots allowed at once.
The most powerful weapon in the game. Also refered to as the charge shot as there is no need to collect weapon energy to power it up as all you need to do is hold down the firing button to charge your blast. It has extremely good range and at max power it does maximum damage to enemies.
Level 1: 4 damage, 40 xp to level up. No limit to shots, unlike Polar Star level 3.
Level 2: 15 damage, 60 xp to level up. Shoots stream. Unlikely you can pull off multiple. Goes through enemies if it kills them.
Level 3: 50+ damage, 200 xp to MAX, 2-beam stream. More than twice as good as level 2. Goes through enemies.
Max: 50 to 100 damage, full-fledged beam. Goes through all non-boss enemies as well as some bosses. Does around 150 damage to big bosses, less to smaller ones.
Missile Launcher
A powerful weapon, especially against boss enemies, although ammunition is limited. Find missile expansions to increase the maximum amount of ammunition you can carry.
Level 1: 8 damage , 10 xp to level up (Note that the rocket launcher does damage to an area).
Level 2: 15 damage, 20 xp to level up.
Level 3: 8 damage, 10 xp to MAX. Range limit one screen, at level 3 shoots 3 rockets per shot, 2 shots on screen at once.
Super Missile Launcher
Super Missile - An upgrade to the Missile Launcher. This does maximum damage at maximum power. Extremely useful against boss enemies.
Level 1: 20+ damage, 30 xp to level up. Same properties as normal Rocket, more damage. I think it might move faster, too. Also damage to a radius.
Level 2: 28+ damage, 60 xp to level up. Bigger Rocket. Still does area-effect damage.
Level 3: 3*14+ damage, 10 xp to MAX. Unsure on damage, it varies by enemy, probably by size. Area-effect, shoots 3 missiles with each button press up to 6 at a time..
Awarded by Santa of Grasstown as thanks for finding his key. This can be useful for enemies that are below you or on a small inclines and slopes.

Fireball (General): Range limit approx. 1 screen, rolls, falls, move while shooting up different from (better than?) not moving. Also can't destroy destroyable blocks.
Level 1: 2 damage , 10 xp to level up. Limit 2 on screen.
Level 2: 6 damage , 20 xp to level up. Limit changes to 3.
Level 3: 6 damage, 20 xp to MAX. Limit 4.

Found in the fireplace in the Assembly Hall of Mimiga Village. Starts off rather weak, but at power level 3 it becomes a very useful weapon since not only do the bubbles create a barrier when holding the firing button down, but releasing it will fire a barage of bubble stars in any direction you are aiming.

Level 1: 1 damage, 10 xp to level up Limit 4, shoots straight ahead. 100 ammo, regenerates slowly (around 2 per second).
Level 2: 2 damage, 20 xp to level up. No limit except speed. Much longer range, spreads, 100 ammo regenerates quickly (around 15 per second). Hold down button to shoot swiftly.
Level 3: 3 damage , 5 xp to level up. Limit 15 shots at once. Bubbles follow around, release to shoot all. Hold down button to shoot fastest. Same ammo regeneration as level 2. Projectiles shoot one screen in length.
A blade that is picked up after finishing Sand Zone. While it has a short range, it is very powerful and at level 3 it can obliterate several groups of enemies at once.
Level 1: 15 damage, 30 xp to level up. 1 shot on screen only!
Level 2: 18 damage, 60 xp to level up. 1 shot on screen only, shorter range than level 1!
Level 3: 18+ damage, 0 xp to max. Phantasmal King with area-effect - stays for approximately 1 second dealing damage to area if it hits anything. Only one on screen. level 2 does more damage per second, but does no area damage. Each hash-thingy does 1 damage per hit, with more damage closer to center. Varies between 30 and 80 damage to bosses, depending on size.
A weapon of some expertise to use. Starts off strongest when at level 1 and becomes significantly weaker as you power it up with weapon energy. It is one of the strongest weapons in the game in terms of damage per second.
Level 1: 12 damage , 1 xp to level up. DO NOT LEVEL UP! Good range (at least half of the screen), good damage. Limit 2 on screen, but they travel fast. Curly uses this later.
Level 2: 6 damage, 1 xp to level up. Again, don't level up! It gets worse. Damage halved, although it's still a decent weapon. Range about the same, limit 3 (I think) but they don't travel as fast.
Level 3: 1 damage, default MAX. If you get to level 3, you can get hurt to go back to level 1. Crappiest weapon ever; 1 damage, less range than level 1 Polar Star, and unimpressive sound. You shoot rubber ducks; it's a wonder they don't heal the enemy.