How to get rid of this path 'oversoot'

If the first and second keyframes have the same value just make the first keyframe a hold keyframe. 

I'll be positng one of my Quick Tips soon on keyframe management.

Make sure the Keys column is visible in the timeline. It is the first column in your screenshot*. 

Navigate to the problem keyframe using the left or right pointer on either side of the diamond. Select that keyframe in the timeline. Zoom in to the timeline if you need to. Now use the Animate menu, or right-click, or use the Keyboard Shortcut Shift + Ctrl/Cmnd + k and set the incoming or outgoing velocity to zero and the influence to zero until you get the results you want. When the motion path is exactly the shape you want but you are getting rebound or unwanted movement between keyframes this is an easier solution than using the Pen tool (g) plus the Alt/Option modifier key to adjust the bezier handles on the motion path.

As Andrew said: * The "Drag & Drop here..." area is buggy and should not be used to share images. Please use the toolbar or just drag your images to the reply field.

I apologise if it's just me, but I can't make head nor tail of your post.  Can you expain the issue with more detail?  Your layer moves faster in the second half of the motion path, but that's presumably just the design of the motion path.

You have three linear Position keyframes and the rest are roving keyframes.  What's going on there?

What is the "delay" slider on your layer linked to? 

Please post images by dragging them directly into your response, rather than adding them as attachments.  It's such a pain to have to keep opening attachments when assessing a problem.