How to set the Tablix outer border width
In your first screenshot, the BorderStyle value is None. In order for the BorderWidth setting to have an effect, the BorderStyle setting must be changed also (e.g. to Solid).

The borders in your second screenshot are cell/row borders. The weight of these borders are controlled via the BorderWidth setting of the cell or row.

The Tablix border is in addition to the cells borders, so if you want the Tablix to have a thinner border than the cells you will need to either use different colours (e.g. LightGrey for the cells and Black for the Tablix), or change the top/bottom/left/right border settings for each outer cell.