How can the cell line contribution be estimated from RNASeq data? Using a laser-capture microdissection of cells a group of cells stained with the marker of interest was sequenced. In another cohort of patients (this is all  human liver tissue) the whole tissue was sequenced (RNA-seq in both cases)

Can I estimate the contribution of the cells marked in the whole liver ("weight of these cells" in the liver in words of my PI)?

My gut feeling is that it can't be done this way, it would require both single cell sequencing and whole tissue sequencing to estimate the contribution of each cell line. But perhaps there is a tool that given the cell lines or the main expression of other cells lines it can be compared to using GSVA or some similar tool.
There are couple of computational methods which try to do this (I never used them, so no experience):


CellMix, based on sets of marker gene lists
Subset Prediction from Enrichment Correlation, which is based on correlations with subset-specific genes across a set of samples.
Cell type enrichment, which uses our highly expressed, cell specific gene database
Cell type-specific significance analysis using differential gene expression for each cell type


You might have to get some reference expression levels from public databases or papers for some of the methods.

One thing to keep in mind: you cannot really compute the cells proportion, only RNA proportion. If you have a good reason to assume that RNA quantity 
per cell is very similar, this is a good proxy for the cells proportion in a tissue.