Hi Dave. And welcome here mate.
It's very easy to get suckered in to buying every bell and whistle of kit and kaboodle when you are just getting started again after long absences from this sport. Firearms dealers are not there to save you money, they want you spending in their shops!
Reflex sights are not going to help you score much with a sub 12 ft/lb air rifle. You won't hit diddly to be honest because an air rifle, especially a spring rifle, has to be carefully aimed and with a precise trigger let-off to release the shot. Not throwing the rifle up into your shoulder and snap-shooting all inside a split second. That's movie bollocks.
You've got a couple of nice Weihrauchs with the 97KT and 99S so now, you need a nice scope or two to set them up right with.. I have a couple of Hawke Panorama scopes for two of mine. Put's the pellet where it needs to be and neither were all that dear. About £130 each.
My Air Arms Pro Sport has near-£500 Nikon Fieldmaster 6-18x40 Side Focus. That scope puts the pellet right into the brain box of a rabbit at serious distances! But a rifle costing £555 of this standard of precision deserves the glassware to match. (And because I'm worth it! 0
How much you are prepared to spend goes a long way in this sport. But you don't have to go spending mega-money to have a great and effective shooting rig. Good quality rifle, decent scope, the right pellet. Everything will fall into place once you have your basic shooting kit right.
DON'T, whatever you do, go wasting good money on shooting rests or bipods for ANY spring rifles.
They don't work to dampen the bounce of the spring's recoil. In fact, they only serve to make it worse and you'll miss your target by a good measure. No matter how much you spend on scopes! Only your leading forehand with the rifle's forestock resting comfortably on it, does that job.
Precision accuracy in your shooting results only from having a proper, top quality rifle and scope, the essentially-correct pellet and a ton of practice on a range, shooting to all distances and getting to know exactly how your pellet's trajectory maps out, from the muzzle end to the dead-on bullseye!
For your HW97KT and 99S try using H&N FIELD TARGET TROPHY pellets. Not many Weihrauch rifles that don't get on with these. My HW97 .177 loves these in 4.50mm headsize. My HW80 and HW77 are both .22 and LOVE 5.53mm headsize H&N FTTs.
Headsize of pellet you want to try makes a fundamental difference in accuracy from your barrel over another headsize pellet that is otherwise, an identical calibre and brand.
You'll find the headsize of pellets on the back or underside of the tin, where you will see a label with a barcode and at the top, is the name of the brand/pellet and the headsize. It will state this as something like (in .22 calibre) 5.52 or 5.51 or 5.53 and so on.
In .177 calibre, the same info on the back of the tin will be found but this will read; 4.50, 4.51 or 4.52 and so on.
Both these little bits of data might not seem much but they are far more important than some might think. These are the microscopic differences from one pellet to another and you gun's barrel will act accordingly with them, either very favourably downrange at the target; or a complete waste of time. Not to mention cash!
And they give you a good idea of Pellet Weight; another factor to consider for pellet accuracy.
It's crucially important to building your shooting accuracy that you know and appreciate this info about your pellet choices headsize, first thing now
All the best and welcome here Dave..