I'm trying to calculate a weighted average using the summary statistics tool using median HH Income census tracts and a single polygon for a target area. So far I have been able to calculate the percentage of overlap for the target area and census tracts, however I'm a bit stuck on the summary statistics tool. I keep getting a frequency of 1 so I'm unable to calculate the weighted average. My statistical field is the percentage of target area times MHH Income, and case field is the Tract Name. Here is a snapshot of the data:

The image seems to have two vector layers, yet you have posted this in the Spatial Analyst Place... If this is in error, it can be moved to Geoprocessing for correct exposure.

In any event. You have a need to bring over the attributes during the overlay process. I would advise you to look at the images and text in

An overview of the Overlay toolset—Help | ArcGIS for Desktop

to decide which approach would yield the results you need. You need the area and pop from the census data and you need to get the geometric intersection and the attributes from the overlay process of the buffer with the census data. If you have the appropriate license level, then you have options.