After a long delay, I am able to post my picture of the mark on this mysterious paperweight and also a picture of the paperweight. The base of the paperweight has a silver plate covering with felt in the center. The base layer is copper and some of the silver has been worn off. The maker of the original glass paperweight is unknown. The focus was on the silver base which has a series of tiny hallmarks. You can see the location of the mark in the last picture (of the base) at approximately 10 o'clock. The paperweight is 2 3/4" diameter by 1 15/16" high. The mark is on a raised area which is 3/16" across.
Since the original posting it has been verified that the mark belongs to a small silver firm Sileda Ltd in Cefn-y-bedd Wales UK. The confirmation of the mark was provided by the Sheffield Assay Office. The makers mark is S.L. with a small indent between the two letters. Sileda registered their punches between 1980 and 2000. It is known that they added silverwork to the base of paperweights, to the collar of vases, and possibly other glass objects. Some of the glass objects have been identified as sourced at UK glass studios. The maker of the glass paperweight does not seem to be identified in my searches. Mike Hunter in one Facebook post commented that they may be a firm he as seen at trade shows and, if so, they had some glass making ability and perhaps made the paperweight themselves. I don't claim any knowledge of UK silver marks, but have been able to identify the first mark below the SL as the Sheffield Tudor Rose (the Assay office in Sheffield), The middle mark is a mystery to me because you would expect a quality mark, so this may be a variation of the lion rampant. The third mark, a script M, establishes the date as 1986.