You can see spatial weights in the map and log by asking the Cancer Atlas Viewer to show you the neighbors of an individual object or a set of objects. For example, the polygons with red borders in the image below are the rook neighbors of the orange-bordered polygon.

The Cancer Atlas Viewer will also add the neighbor IDs and their weight values to the log. Something like this will appear: "Neighbor ids of object 458 using spatial weight set, 1st order rook: 456, weight=0.20; 457, weight=0.20; 458, weight=0.20; 459, weight=0.20; 460, weight=0.20". The ID values will be the Object ID dataset, visible in the table or by querying the object in the map.
Right click on a map and choose "Show object neighbors". If there are multiple layers in the map and multiple weights sets, you will need to choose a weights set for each layer you want to see. This turns on the "Show neighbors" functionality.

Next, each object you click on
using the selection pointer will be highlighted in the selection
color, and its neighbors will be highlighted in red and the weights
reported in the log.
If ego is included, then
the selected area will also be highlighted in red and it will be listed
as a neighbor and have a weight in the log. You can Shift-select several
objects to view several sets of neighbors at once.
You can zoom,
pan, and query
as usual, but the selection pointer will select objects and show their
neighbors in red until you turn off the functionality.
To stop, right click on the map, choose "Show object neighbors" and then uncheck the chosen weights set(s). When all sets have been cleared, the selection pointer returns to its normal state.