LM22678 Unstable output
"what I am doing wrong"? - it is likely a sum of small deviations from recommendations of manufacturer. You are not following the recommended layout and details of their component suggestions. You are using non-SMD D1 (inductive leads), the output cap looks too small, input caps are recommended to be at least 2 X 6.8 uF ceramic (webbench comes out with 3 x 22 uF caps, you have only one), and you didn't mention anything about your inductor (pads are too small for a proper inductor).

You need to examine carefully the fundamental current-flow diagram presented in the LM22678 datasheet:

 

As the datasheet says:


  Board layout is critical for the proper operation of switching power
  supplies The most important layout rule is to keep the ac current
  loops as small as possible


Please trace the current loops as they develop on your PCB, you will find that they are far from optimal.

Addition: here is the WB suggested layout:



While the BOM lists DO-201 package for diode, the layout shows SMD (funny, pictured in opposite direction). Also, there is no need for massive ground trace coming around the inductor, the capacitance of this fast switching node must be minimized. You also should try to characterise your design not just for "no-load" and "full-load", but try to load it gradually to see, where it starts barfing.

Best thing is to get their reference design, and copy exactly everything.