You can see spatial weights in the map and log by asking STIS to show you the neighbors of an individual object or a set of objects. For example, the polygons with blue borders in the image below are the first-order rook neighbors of the orange-bordered polygon. Using the "Show object neighbors" function will also add the neighbor IDs and their weights to the log (see bottom of image, below). The numbers shown before the weights values will be from the ID dataset, which is also visible in the table, or by querying the object in the map (if you need a reminder of the name of the ID dataset in your project, check the top of the log).

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. The weight selection step turns on the "Show neighbors" functionality.
Next, each object you click on using the selection
pointer will be highlighted in the selection
color (orange is the default), and its neighbors will be highlighted
in blue, with the weights reported in the log.
If ego is included in your
weight calculation, then the selected area will also be highlighted in
blue, 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 showing neighbors, 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.