Opacity keyframes are snapping when

Are any of the keyframes identical -- like, it's actually holding for a bit before moving on to the next one? If there was a hold followed by a sudden move to a new position that could come across as a "snap."

Also, are you zoomed in all the way in the effects tab to see all of the keyframes? There's a possibility that you have two keyframes really close together, which might account for the snap as well. You can find this out by using the right arrow next to the keyframe button; the playhead will go to the next keyframe each time you press it. If the playhead barely moves at any point then there's an extra keyframe hiding in there.

Finally: if all esle fails, go back to the last "smooth" keyframe and delete all the ones past that, and redo them. Sometimes the only solution to keyframe shenanigans is to start over. Keep in mind that all of this is much easier in After Effects, and there's even a graph editor where you can see and correct any weird movements between keyframes; might be worth your time to learn masking and tracking in AE if you're doing this kind of work a lot.

HTH,

JVK