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Based on my experience, zoom-in and outs of large files are generally the number one culprit in performance slowdowns. In your animation, between the zoom-out on the ball and background and the animations on the balls (multiple fade transitions and rotations), there's a lot to process at once. My first couple of suggestions are to decrease the the file size on the background image (the tree) and then to only begin the ball animations once the zoom out has completed. I'm guessing the background image is the 500kb image you referred to. Try taking it down to whatever quality is best before it's noticeably compromised. There's no fast rule for appropriate sizes – much of its depends on what you want to do with it and the platform it's going to run on. For instance, I noticed that the animation runs smoothly in Chrome while it has the hardest time in Firefox.
If you've eliminated any issues resulting from what Brice has suggested, one thing that I regularly find causes jerking is if I've unintentionally applied easing to animations. If you've got something like In-Out Elastic easing it could certainly create the effects that you're getting there on some of those animations, though it might not explain all of them. Probably be worth sharing the composition to have someone take a look at it.