Fixed Power Scope for Henry H001 22 Lever Action

2.5 x Bushnell banner scope, if you can find one.

I wouldn't spend much on a fixed power .22 scope. Not sure on the price of the primary arms scope, but if you like the acss I would get it. Even the cheapest chink scope can handle .22.

Grab any decent 4X32 scope; I use Bushnell and Simmons because I can pick them up at a Bushnell outlet nearby for $10 each. I particular like the ones that have a "focus" eyepiece.

I have the same rifle and they are indeed nice shooters. Put a rail on mine and was considering a fixed 4x or a 2-7x rimfire scope when I came across an inexpensive Tasco Red Dot on sale. Never owned a red dot and figured it's time to try one out and if I don't like it I'm not out much money. Put it on in early 2019 and it's still there after I discovered how much fun they can be on a .22. The step grand daughter likes it, too. Although I think there will be a winter project coming up after deer season with a rimfire scope ( 2-7x maybe? ), for next year. Even if I go back to irons that little Henry will be out plinking next spring, or perhaps squirrel hunting this fall. Here's the step grand daughter ventilating 12 oz. aluminum pop cans a few months ago. .. My only complaint is that the red dot unit almost looks too big on a trim little Henry H001 rimfire lever but it really is lots of fun. Be interesting to see a compact rimfire scope on there. As long as it's not overly big for the size of the Henry.

Honestly, if you're only shooting out to 50 yds, you don't need a scope. If you want to upgrade your sighting system, why don't you take a look at replacing the rear sight with a Skinner peep sight. Perfect for 50 yds (or more).
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You'll do better money wise to buy a 2-7X variable than a fixed power scope. Most fixed power scopes are either junk or high end. Lots of options for decent quality 2-7X or 3-9X scopes. If you really want it small a 1-4X is going to be lighter than most fixed powers. But I'm not aware of any decent 1-4X's priced under $200. You can find a 2-7X or 3-9X of decent quality for around $130-$150. I wouldn't touch anything cheaper.

Swift 4x32 @ $80 on Amazon
Swift 4x40 @ $120 on Amazon
Vortex Diamondback 1.75-5x32 @ $180 on the web.

i have 2 bushnell scopes that work well. one is a fixed 4 and the other is a 1.5 -4.5 and it works well also. Both are parallax set at 100 yards which i dont really like for rimfire. they used to make them for shotgun set at 50 which would be a better choice for you

https://us.hawkeoptics.com/vantage-4x32-3030.html

This may be an option.

I have a Simmons 4 x 32 rimfire scope on a Uberti Silverboy and its great for plinking.