Cell Data and Point Data integration process

Hello all,
I’m struggling with Cell Data and Point Data. I made a python script to compute mass-weighted average of some varaibles over a given set of slices. It works great with an input solution with cell data, but gives poor results as I start from point data. My problem is that I need to correctly compute cell values starting from a point data solution.
The point-to-cell filter does not help, admitting errors in the averaging process from nodes to cell (I have an unstructured grid). Same happens without the filter, during the execution of the script. My guess is that the integration process that I perform through integrateVariables admits an error too, somehow needing to obtain cell values (area) from point data. How does the integrateVariables filter work?

To expand on my problem, I have a dataset of point data for a given surface, and I can also have a dataset of the correct cell-center values, which I’m able to load as an ascii and transform with TabletoPoints into a set of unconnected points. Is there a way to tell my original data-set to get those correct values as cell-center values, instead of applying point2cell filter?
I tried some combination of resample with dataset and append attributes but with no success.
Hope I made myself sufficiently clear.

Thanks for any help.