Behavior:
Polylines are a very old issue with Revit since it was developed...for some reason Revit seems unable to translate the width/type of polylines (in general) on its own. So how if its 1 line with several segments on 1 linetype and various width for each segment maybe because Revit reads lines, layers and coordinates differently than CAD.
Thinking out loud; from that attached photo it appears that you used a lightweight polyline. As such the vertices don't have a Z value where Z is an essential input in Revit. And LW Plines appear to be one of the few if not the only which has no Z Value (not even 0) And this doesn't exist in Revit... ie: missing input => wrong behavior...Nonetheless, this is my personal assumption and best if Autodesk Development would confirm
Suggestion:
One known workaround for polylines with uniform width (example: room boundaries; filled regions...): You can inn AutoCAD place the Polylines of similar width/Linetypes on their own AutoCAD Layer and then under "Object Styles >> Imported Objects" tab assign a specific thickness and line pattern to that specific Layer. Then Revit should be easily able to translate it.
For Polylines with variable width verticies: (I haven't done this personally but I've seen it on several Revit Blogs) one can resort to scripting a code (.NET) to translate the properties of each segment/vertex in the PLine so Revit can then read it...I think it has to be done pre- Revit API...You may want to check in the AutoCAD forums. I know there are for sure coding methods which can introduce functions like Vertices to Points something like Read Geometry in Python to extract/read/translate the info of X,Y geometries (such as LW_PLines) into an X Y Z for each vertex in the geometry readable by other softwares.