The Warne 30mm Fixed PA Rifle Scope Rings low height rings measure at 0.250" from base to saddle. Medium height rings measure at 0.375" from base to saddle, and high height rings measure 0.525" from base to saddle.
These rings will fit both Picatinny & Weaver style bases. These will not fit the factory dovetail of the Marlin 883.
The high height is going to be the best recommendation to stay away from making contact with the barrel and still allow you to have room for lens caps if they are being used.
Yes, these fit both Picatinny & Weaver style bases, so they will fit your Burris Weaver bases. Both heights should work per Warne's specs, but I would recommend MPN: 515M to put you at a safe height above your barrel and action.
The high height is going to be the best recommendation to stay away from making contact with the barrel and still allow you to have room for lens caps if they are being used.
The low have a .250 saddle height which would make the height from the bottom of the ring to the center split approximately .841".
Yes, these rings will fit the standard cantilever mount for a Remington 1187.
What a great question! Wonder why OP doesn't list this - pretty important. I suggest you visit the Warne (or Talley, etc.) website and get the dimensions from the manufacturer. That's really the best source.