Scope Jesus?…that’s funnyAhhh, 'Scope Jesus' says it's bad. You've never actually had one though...
It's a scope I wouldn't dial with and that was not my recommendation. Just offering something different. Best of luck to the OP it's a list that may be hard to fill - everything is a compromise.
I’ve had Zeiss Conquest, not the V4. Had problems with it on 7mmRM and 300WM. I’ve had issues with other scopes as well. What “Scope Jesus” promulgates makes sense and, unfortunately, I’ve experienced some of those issues but always wrote it off to other things.
A scope you “wouldn’t dial with” is indicative of design issues with the erector system that would also mean issues with keeping zero. Yup, I’ve experienced that as well.
For BCD:
Look at NF, SWFA, Bushnell LRHSi/LRTSi 3-12 (if you can find them used for sale - I now have 3), possibly Trijicon Credo’s (soon to be tested by “Scope Jesus”).
NF SHV 4-14 F1 meets all your criteria except weight (it is 30 oz).
NF NXS 2.5-10 is SFP only and weighs in at 19 oz. Blows your budget though.
SWFA 5-20 can be had illuminated, but blows your budget as well as weight criteria (31 oz).
LRHSi are about 26oz
Trijicon Credo 2-10x36 FFP is mRad, about 23 oz and is right around your budget (I have one and like it so far)
If you haven’t read the Scope Evaluation threads, they have a lot of great information