drawing a weighed network

[Mariano Devoto]

Dear All,
a question from a dummy to the experts. I'm trying to draw two sets of
rectangles of different sizes aligned in two rows and "connect" some
rectangles in the upper row with certain rectangles in the lower row using
triangles of different size (or lines of different thickness). Something
similar to a flow chart, I guess. Also need to add a label to each
rectangle. Sizes, positions and thicknesses are all determined by values
in a matrix. What I'm trying to depict is a weighed bipartite (aka
two-mode) network. Any ideas regarding what basic functions should I learn
to use? Sorry for this very basic question.
Thanks for your help!
Mariano