Was curious about how much better different rarities are, so I crunched some numbers. This should help you understand how weapons scale with level and rarity, and when you should swap out for something new, even if it's a lower rarity.

I only tested this with one weapon type and not armor. If I feel like collecting more data for those later I may update the guide but for now I'll just assume the numbers are similar for all weapons and armor.

white = +0 levels
blue = +2.2 levels
green = +4.2 levels
purple = +5.8 levels
pink = +7.3 levels

To start, damage scales exponentially with level. I don't have an exact equation, but it's your typical "you get more per-level at higher levels than you do at lower levels". Rarity seems to increase your position on this graph by a static amount, not a multiplier. So a higher rarity item will always be "approximately the same as a lower rarity item plus x levels". This also seems to be the same for both higher and lower level items. So it's the same increase at level 20 as it is at level 60. Crafted levels function the same as base levels.

A blue weapon will always be about the same as a white weapon 2.2 levels higher than it. So a white 23 is just a bit better than a blue 20.

A green weapon will always be about the same as a blue weapon 2 levels higher than it. So a blue 23 is just a bit better than a green 20.

A purple weapon will always be about the same as a green weapon 1.6 levels higher than it. So a green 22 is just a bit better than a purple 20.

A pink weapon will always be about the same as a purple weapon 1.5 levels higher than it. So a purple 22 is just a bit better than a pink 20.

Notice the increase gets smaller with higher rarity. So single steps will round to about 2 levels, but larger steps will not always move as evenly. More exact numbers are here:
blue = white+2.2
green = white+4.2, blue+2.0
purple = white+5.8, blue+3.6, green+1.6
pink = white+7.3, blue+5.1, green+3.1, purple+1.5

So if you find a blue whose base level is 6+ higher than your pink's base it will actually be a small upgrade.

So to back this up here's the raw data I concluded this from, all the same weapon, just different levels and rarities. Could use a larger sample size but I feel it's good enough to make some quick comparisons while playing:

g 41 571
g 42 612
g 43 656
g 45 754

p 41 642

w 20 99
w 21 107
w 22 114
w 23 123
w 24 131
w 25 141
w 26 151
w 27 162
w 28 174
w 29 186
w 30 199

b 20 116

g 20 133
g 21 142
g 22 153

p 20 149
p 21 160
p 22 172
p 23 184
p 24 197

u 20 166

This is the dps for various weapon types. This was tested on white level 40 weapons with no runes equipped. I had to calculate backwards to account for perks.

Battle Axes: 366-448 melee physical
Boomerang: 366-448 melee physical
Great Sword: 366-448 melee physical
Katars: 513-627 melee physical
Lance: 366-448 melee physical
Sword: 366-448 melee physical
Demon Sword: 366-448 melee magic
Magic Sword: 366-448 melee magic
Bow: 369-451 ranged physical
Pistol: 369-451 ranged physical
Throwing Daggers: 443-541 ranged physical
Alchemy Bomb: 369-451 ranged magic
Demon Bow: 443-541 ranged magic
Fireball Staff: 295-360 ranged magic
Spellbook: 184-225 ranged magic