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To do this I would use the Union tool to calculate the overlap relationships between polygons. I would then use arcpy.da.UpdateCursor to iterate through each polygon and add up the ranks/weights of any polygons that overlap in that area.
I think dwell time and trajectory are more appropriate words for this. See "Estimating the most likely space–time paths, dwell times and path uncertainties from vehicle trajectory data: A time geographic method". -- Tang J, Song Y, Miller HJ, Zhou X (2015)
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