If you have the full 3/16 gap (I am using our American unit because I don't have the codebook here to make sure I use the correct metric equivalent) instead of surfaces in contact then you increase the weld size by the amount of the full gap not just the amount over 1/16.

So, yes, if your drawing calls for a 1/4" (I believe that is correct for 6mm)  then you would increase it to a 7/16" fillet weld (9mm)

For engineering purposes there is no strength calculation for the amount of weld that MAY be of decent fusion in the gap.  The only measurement that matters is the leg and since 3/16" of the leg is in open space there is not much holding the part; only 1/16" theoretically in this example. So, you add the amount of gap to get the correct amount of strength from the weld.

The code does allow the gap to be 1/16" with no added weld needed but beyond that you must add the amount of the entire gap not just the amount over 1/16"

He Is In Control, Have a Great Day,  Brent