Evolution has two tiers: first awakening, then ascension. If you want to take a weapon all the way, you have to aim for both.
Two Tiers
Once you've grown your weapon and its paired passive enough, the awakening card shows up first. Above that sits a second tier: ascension. Most similar games have a single tier; here, the second tier is where the real late-run power is.
If the Card Won't Show Up
The evolution threshold is set by the highest level the paired passive can reach. So a weapon paired with a low-cap passive evolves at an earlier level. If you've maxed the passive and the card still won't show up, it's the weapon's level that's short.
You'll Notice the Evolution
An evolved weapon doesn't just hit harder: it changes noticeably on screen, in the HUD and in its sound. If you're not sure anything changed after taking a card, you most likely took a normal level, not an evolution.
It Doesn't Get Lost in the Crowd
However full the screen gets, every active weapon stays both audible and visible. The game turns down ambient effects for performance, but never weapon feedback — if you can't see a weapon on screen at all, it really isn't firing.
Don't put off the awakening card when it shows up. Evolution carries the rest of the run; the earlier you take it, the longer it works for you.