Hi Mike, as already pointed out this version of the gun was known to Beeman as the "HW 55 MM". The "M" designates the basic Bayern-style Match stock which has been around since the very earliest days of the HW 55 in the early 1950's.
I would guess yours is a pretty early example with the fore end accessory rail, which was added to the M after the HW 55 CM with modern match stock was introduced in the mid-1970's (see pic below). The rail is the standard Anschutz profile and can take a bunch of different accessories; I use a small target bipod frequently (lets you set the gun down without having to lay it on the wood), and the HW 55 is a ball to shoot with a palm rest.
A gun of that vintage will almost certainly have leather piston and breech seals. These work VERY WELL in the 55 and I wouldn't change either one unless necessary, just re-condition and lube (but, if you do need to replace one, not much of a problem, the parts are out there). Note that the breech seal fits very closely--when correctly fit, you can just barely see that it's proud of the metal breech face, which is quite different from HW's sporter rifles.
I highly recommend the spring/guide kits that Jim Maccari makes for this gun--a solid improvement to Weihrauch's best-ever rifle.
I am NOT an expert mechanic or qualified tuner, but I have taken apart and re-assembled a bunch of HW 55's! I'd be very happy to help if I can, please contact me off-forum if you'd like.