I have a polygon feature class representing discontinuous fields (see below), I would like to make a heatmap based on the distribution of these polygons. I'm using Arcmap 10.2.2 and am aware of the methods to make a heatmap from point data but I'd like the heatmap to take into consideration the size of each site.
You will still need to convert the polygons into the points if you want to create a heatmap from points versus using gradient symbology on your polygons.
Here are two options (there may be more) you have:
Add a new field to the polygon feature layer and calculate the area of each polygon.
If you have Advanced license, run the Feature To Point GP tool which will create a new point feature class with the newly created area field preserved. Now you can use your Kernel Density or any other method for creating heatmaps when you can take into consideration the area field value.
If you do not have Advanced license, then create two fields of Double type and calculate them to have centroids of the polygons. Then export the layer into a non-spatial table and then create an event layer from this XY table. Now you have a point feature layer with the area field (more help on this here). Again, ready to create heatmaps from this.