My understanding is that increased bullet weight increases pressure. My understanding is that gas checks increase pressure as well. So, why would the published powder load, in this case IMR 4227, be greater for a cast bullet with a gas check vs its counterpart, it also being cast but of lesser weight and with no gas check?
To sum up your questions...
Increased bullet weight does, indeed, increase pressure. That's why you will see load charges go down for a heavier bullet, when comparing apples to apples... that is, say a Hornady jacketed bullet vs a Hornady jacketed bullet.
Gas checks seal the base of the bullet, much like a jacketed bullet obturates... increasing pressure with a better seal. The benefits of a gas check are two-fold... besides a better seal, you can generally drive gas checked bullets for this reason, and as was mentioned, reduce leading from a hot flame front.
Cast bullets can run from very soft (pure lead) to very hard (typically called 'hard cast.') There are benefits to both... depending on what your purpose is for the bullet, and how fast you plan on driving them. Again... generally speaking, soft lead bullets cannot be driven over the generic threshold of 1200fps (or even less...) without leading and other problems. Harder cast bullets can... I regularly drive non-gas checked cast bullets into the 1800's, and gas checked cast over 2200fps.
There are also exceptions... like the .45 Colt. A generic .45 Colt load won't drive any bullet over 900fps (or thereabouts, depending on the weight) but there are firearms that can handle heavier loads, and data is provided for those specific firearms... using the very same bullet in some instances.