How can I know the effect of a weapon ability?

There's no in-game explanation, but I found most of them pretty obvious based on things that happened to me during Solo. For example Shaking is when your aiming reticle starts shaking and jumping all over the screen.

There's an image floating around various message boards that does explain them all:

Offensive

• Shot range: Increase the distance your shots travel
• Shot homing: Increase the homing ability of weapons, if they have any to begin with
• Various attacks: Increase the power of that kind of attack
• In-peril attack boost: Raise attack when your health is low
• Full-health boost: Raise attack power when your health is full
• Shot cancellation: Increase ability to cancel incoming fire
• Power attack: Increase damage done by attack powers
• Item attack: Increase damage done by offensive items

Defensive

• Overall defense: Reduce the amount of damage received
• Melee defense: Reduce the amount of damage received from melee attacks
• Shot defense: Reduce the amount of damage received from ranged attacks
• Knockback defense: Reduce the chance of getting knocked down
• Evasion: Increase the size of your dodge window
• Health: Increase your max health
• In-peril autododge: When your health is low, you will sometimes automatically dodge

Status Effects

• Confusion: Causes reticle or movement to be inverted
• Petrification: Target turns to stone; they can't move and defense increases
• Freezing: Target is unable to move
• Paralysis: Target speed is reduced
• Shaking: Target's reticle goes haywire
• Burning: Small damage-over-time from fire
• Poison: Small damage-over-time from poison
• Weakening: Target's health max is halved
• Recovery effect: Status effects do not apply to you as long
• Status resistance: Status effects are less likely to apply to you

Movement

• Speed: Increases all movement speed
• Walking speed: Increases only walking speed
• Running speed: Increases only running speed
• Stamina: Increases the time you can run for

Other

• Self-injury: Your health is constantly draining, similar to poison.