C801tfd: OK - you officially get the prize for bargain of the century! Beautiful classic target air rifle...basically for free! Wow.
As R1 lover mentioned, that is a late-model gun with improved stock geometry; earlier 55M's don't have as much drop at the heel of the stock. The later version like yours works better for most folks.
A few words about sights:
+ Your late gun definitely has the "11 mm" scope grooves. The old HW match rear sights were made in both 11mm and 13mm widths, so if you get one of these be sure to verify it's the right model.
+ If you aren't fanatic about OEM accessories, Anschutz sights, both front and rear, fit just fine on the HW 55. They are somewhat easier to find and IMHO have certain functional advantages.
+ This shot shows an HW 55M with an HW sight on top, and one with an Anschutz sight on the bottom. The Anschutz uses an 18mm thread on the securing sleeve, while the older HW design is 17mm. There are still a full range of accessories made for 18 mm sights, such as the neat and inexpensive clear acrylic ring inserts seen in the photo. With the 17mm sight, you will be limited to the original Weihrauch metal inserts.
+ Here is an HW rear diopter sight. Nice sight for sure, but note how it drops down below the top line of the receiver, limiting where your thumb can go! Also, the sight is limited to one of three positions (the big flat thumbscrew on the top front of the sight, fits into one of the three holes on top of the receiver).
+ Here is an Anschutz rear sight on an HW 55. It's a bit more compact, adjusts very precisely, and leaves the space behind the receiver tube open. The mount is a simple and very strong clamping action that can be placed in any position you want. These were made in several models back in the day, which look different but work basically the same. The eyeshade on this one is an aftermarket accessory.
Both rear sights use the same standard thread (9.5 x 1.0mm) for the eyepiece. These will interchange between brands, and there is a whole universe of cool adjustable-opening irises and other accessories made for them (my avatar pic is this same sight, using an old Gehmann iris with magnifying lens).