A weapon (or defensive equipment) can be upgraded easilly up to +4. After +4 there's a chance that the weapon will break.

Upgrade Chance and Effects
First off, the general upgrading chance works like this:
"The following is speculation"
From information taken from different players, the success rate of the upgrade system works by %, and this list is the most accurate up to today.

Upgrade Level....Success Rate....AR/DR Bonus
+1.....................100%..............none
+2.....................100%..............none
+3.....................100%..............none
+4.....................100%..............none
+5.......................50%..............+1
+6.......................25%..............+2
+7.......................12%..............+3
+8.........................6%..............+4
+9.........................3%..............+6
+10.......................1%..............+9


A weapon will glow depending on the level of the upgrade -
Weapons of level 1 to 4 won't have a glowing effect.

+5	White Glow
+6	Golden Glow
+7	Red Glow
+8	Red glow and white shine
+9	Complete rainbow glow, and full white shine.
+10

Note: These pictures were taken with all the options in minimum. +5 Unique weapons will have the +8 White shine with a white base glow.

Strengthening Accelerators
Currently, these accelerators cost 120 gold apiece in the cash shop. So what do they do? Well, their description is a little misleading and doesn't belie their true nature, so hopefully this guide will help.

Rating....N
26+.......20
25.........17
24.........15
23.........13
22.........11
21..........9
18-20.....4
14-17.....3
9-13.......2
1-8.........1

N is the number of str accelerators you'd need to use to double your success rate. It's also the max amount of accelerators you can use for that particular grade of AR/DR. So at +4->+5 it doubles from 50% to 99%, +5->+6 it doubles from 25% to 50%.

Keep in mind, any time you upgrade over +4, regardless of str accelerator, you still have a 1% chance of breaking the item.

Warning!!
You might have seen the laquers from the cash shop (the +5 and +6 laquer) will only protect the weapon from breaking if the upgrade FAILS from +5 to +6 (for the +5 laquer) or +6 to +7 (for the +6 laquer). If the upgrade fails, the weapon will go back to being a normal weapon (a +0 weapon) and the laquer will be consumed.
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What do I get for upgrading?
Every weapon upgraded after +5, will give the character an additional Attack Level/Defense Level (AR/DR). +5 will give 1, +6 will give 2, etc.

Also an incresed Attack/Defense (depending on the item that was upgraded)

Upgrade Increments
Different weapons have different ATK increases per upgrade. Armor give +1 defense power per upgrade. Gloves and shoes cannot be upgraded.

Weapon.............................ATK per Upgrade

• 1h sword:.................+3
• Epee:.......................+3
• Saber:......................+4
• 2h Sword:................+5
• Polearm:..................+5
• Dagger:....................+2
• Main Gauche:..........+2
• Rifle:.........................+5
• Pistol:.......................+4
• Shotgun:..................+4
• Cannon:...................+6
• Staff:........................+3
• Rod:.........................+3
• Bracelet:..................+4
• Knuckle: .................+2
• Leg Guard: ............+2

Note: Info taken from the guide made by Imac2much in the official forums. Thanks to him, we have this information.