Logan, I presume that is your name since you didn't correct it's use in previous post,
If you look at Lawrence's attachment, it shows (E) which represents weld size and in this application for groove welds regardless of J or Flare it is for the depth of weld thickness. That is the weld size.
Now, if you picture that with S(E) the 'S' is for depth of bevel and the 'E' in parenthesis is for weld size which depending upon welding process, type of joint, etc will not always be equal numbers but can be. Since your .19 is in parenthesis it is for the weld size and as that decimal is just slightly over 3/16 I used the fraction to indicate size of weld (rambling more to myself as you probably know most of this, just clarifying my earlier post with the new information). And yes, if they had wanted extra material in the form of a fillet weld or surfacing weld they would have had to add the extension for additional weld symbol.
By adding the convex finish symbol they are indicating they do indeed want a somewhat convex finish which can be done naturally or artificially by grinding, chipping, etc but doesn't need to be if it is acceptable in the as welded condition.
Good luck with the project.
He Is In Control, Have a Great Day, Brent