Here it says that I can get width (of columns I guess) but only thing I can get is the columns IDs.
grid.getState()
Edit:
The response of Ext.encode(grid.getState())
{"columns":[{"id":"280"},{"id":"279"}],"sort":{"property":"DEPARTMAN_NO","direction":"ASC","root":"data"}}
If your original column width is not changed getState
does not return width info for this column.