I think what you're referring to isn't actually recoil, but recoil velocity. The heavier rounds tend to have less recoil velocity, because of the lowered velocity. A hot 240 grain .44 and a hot 300 grain .44 out of my dad's Taurus exhibit this felt recoil phenomenon. It was the same powder, same bullet manufacturer, etc. You get a push instead of a snap.
In my experience, this can get negated with the velocities from rifle cartridges. Once you start putting heavy bullets in at their standard respective velocities, you get more felt recoil because the recoil velocity is still high enough to pop you, but you get a heavier total weight moving out of the bore as well. You don't get that trade-off.
Case capacity has a lot to do with it as well. In pistol cartridges, bigger bullets take up more powder space than smaller bullets, once you start loading with case-filling powders. If you're not using case-filling powders in your rifle, you may be able to get a higher charge with the heavier bullet than if you were using a straight case. This "theory" is also based on published data. I'm not saying to cram more powder in just because it fits.
As you can see, there are a multitude of factors that go into felt recoil. If two powders are loaded to the same velocity in a given round, but 1 is 25% heavier than the other, the heavier charge weight will recoil more, because there is more mass leaving the barrel. You'll also likely get more muzzle blast and flash, given that powders that require more weight per velocity are usually the slower burners. That's not always true either.
The bullet weight is far from the only factor in recoil. You didn't state if you are a hand loader or if you are buying factory ammunition. To build on Brian's point, there's usually a reason that reduced recoil rifle ammunition is not offered in the heavy-weight bullets for a given caliber. It's easier to make a lighter bullet kick less than a heavy bullet. It's also easier to get a lighter bullet to expand properly at lower velocities than a heavier bullet. The engineering challenges are easier.