Size over lifetime jumping to max size from zero immediately

I'm trying to start my particles small and make them get bigger over time. I've already seen this question's answer but no avail: http://answers.unity3d.com/questions/1254165/change-size-over-lifetime-for-particle-system.html

Here is my curve:

All my particles start invisible, and at some point on this curve, they become visible immediately at the full size. So they don't grow from small to big, they just appear at fullsize. When I play with the curve, the "appearing threshold" changes: the particles appear at fullsize sooner or later, but still, it's either fullsize or none. So the curves do have some influence, but I can't figure out what is wrong.

What could I be doing wrong?