The Weaver T09 base is contoured to fit the receiver of a Ruger 10/22, and attaches with screws to the factory-drilled holes.
The #12 looks like one of about a zillion different bases that Weaver manufactures, contoured and hole-spaced for specific firearms. If the bottom contour matches the curve of your Marlin's receiver, it could be used but only by drilling and tapping appropriate holes in the receiver. It's a two-piece base, and each piece requires two screw holes. Trust me, there are easier ways to mount a scope on a $150 .22 rifle.
Unless you absolutely, positively must use Burris Sig rings, how about considering a one-piece base/ring combo designed for airguns and rimfires? UTG makes them, along with other manufacturers. They can be relatively expensive if you buy the ones intended for top-level, high-recoil spring-powered airguns, but the simplest, cheapest ones work just fine on a .22. They do not use the polymer inserts of the Signature rings, but they're machined in one piece...the rings are in perfect alignment, and will not torque or damage your scope tube. You can lap them if you like, but it's certainly not necessary.
Okay, I just checked out the D&L Airgun website. Browse around there and you will see everything you need. They have a couple of rimfire-to-Weaver adaptors that look lower than the one you found earlier (and will allow the use of the Burris Sig Zee rings), as well as a selection of one-piece mounts. They have $100+ Theoben mounts (which won't do anything for you on a .22) as well as $25-$30 dollar Leapers/Gamo/SunOptics jobs that will serve you well. I've dealt with D&L and will do so again...no problems.
And thanks for bringing this thread back, because while checking their website I found just the little gizmo I've been searching for to complete one of my DIY Bubba projects.