I press the T key, which takes me to the targeting screen where I press the select target button. Then I press the W key following which I click on the weapon. At this point nothing happens.
The unit has either no suppression or Ready status.
Then I press the W key following which I click on the weapon.
This might be the problem. After pressing the W key, you need to select the weapon by selecting a number [1-4] from the keyboard - clicking with mouse does not work in this case.