For the tiny or even zero area faces it sometimes seems that not the whole boundary is selected but it is and welding works here also on your flle.
Indeed! I was disdurbed by the way it looked so I didn't even tried to weld.
Btw, is there a simple way to get rid of those needle shaped triangles?
For the second, third... welding you also can select the whole FaceGroups (for each now owns a single boundary) that's easier.
Clever! Another way that works (when turns are far away enough) is to select turn tips using a big volumetric brush.