Shape-wise the bowl of this spoon looks to be 17th Century when around the 1650’s the bowl became elongated, from the previous pear-shape, into a regular ellipse. If this be the case then, on British forms, the handle would normally be flat and broad and divided such that the end became trefoil-looking. On your example the handle is a plain shaft - this would intimate an earlier date (pre-1660). The overshoot of the two forms might indicate that the spoon is of the transition period - 1650-1660. This is assuming that the spoon is of British origin. If it is of continental origin then it is likely to be of later manufacture, as designs took some time to migrate - but it would still probably be of pre-1700 manufacture. At this point I am taking your statement that the spoon has been in your family’s possession since at least 1800. I make this note as the “hallmark” impression looks like a smiley to me and would make me wonder if this is an elaborate fake.Although one of the marks at the base of the handle is extremely rubbed it is probable that they are a double stamp of the same “makers” mark - reminiscent of Scottish custom. The photographs are not good enough to show the mark at the end of the handle to make any conjecture. The marks being on the reverse of the handle, however, make me wonder if it is of later date. If you could get further pictures to me I can possibly make further analysis. There do seem to be some inconsistencies in the evidence so the conjecture that it is of Scandinavian origin may be prudent.