Not sure if linking to a thread in another Bersa forum is a no-no here or not, but here's a discussion about certain Bersas being able to accept Sig Sauer 220/226 sights. I'm no gunsmith, but according to this thread, you can choose from tritium, fiber optic, adjustable rear sights, etc.
(link deleted per Admin...)
Moderator: if this is frowned upon, just delete it and I'll get the hint.
I had a BTUC40 that had this exact same problem. Weird thing was, I NEVER had this problem with ANY of my other BT's. After many rounds and much time has passed, I finally gave up on it and traded it for a BT Plus.
If your serial #starts with # A80077 or higher the sig sights will fit. Go here, then at the bottom of the page is the info you want. The stock sights for me were junk. They are made to cover the POI. I put the #9 rear sight on mine and really like the weapon now. I aim bout 1/2 inch under where I want to hit at 21'. With the new rear sight I start with this and end up with that. Be careful when you remove the sight, it comes out and goes on from the left side and you MIGHT have a spring under the rear sight.
We are going shooting Saturday. I am going to shoot some different brands of ammo. I am 98% sure I am not flinching. there is no reason to pull or flinch. This gun shoots super smooth. Probably the smoothest in my arsenal next to my 1911. I will post my trials and results. I am not going to give up on it as I love the way this gun feels. Will look into some dif sights depending on what I see on Saturday.