Briot is reported to have had a lot of problems with his weights, with a significant percentage of pieces rejected for being out of spec. For some reason you don't often see marks which could be adjudged to be adjustment marks being applied to the hammered tower issues, so it begs the question whether politics came into play here as there is ample evidence of a wide range of weights occurring.
Half a century later, the recoinage during William III's reign produced a serious number of coins with these marks, though the obverses were often filed through the hair or drapery and the reverses at the crowns and not across the centres. This difference may have been due to individual worker preference. e.g see 16(9/6)6 shilling below.
I don't think there is any consistency in where the marks are applied, as I have also seen Briot pieces with the rims filed. Again, see below.