The subsidy is currently 5,000,000,000 units, giving you a lot of dynamic range to play with. That will not always be true. And rounding to the "nearest" satoshi can be gamed, for trivial gain at first to be sure.
It is obvious to me that by the time the generation reward is significantly reduced, satoshis will be split so what is now known as 1 bitcoin will be more than 100,000,000 atomic units. Even in the highly unlikely case that a satoshi will be significant, since the value is rounded down, this will only create a preference to weights which result in an integer, which causes no harm.
Once again, implementation should follow design, and the "2.1E+15 atomic units" detail can be changed.
Also, I'm pretty sure that your idea will create total chaos. Not less forks, but more. Lots more. Like on nearly every block. Not at first, necessarily, but as the subsidy shrinks relative to the transaction fees for sure.
Did I say it will create less forks? I predict that the equilibrium found will be less than 10 minutes, which means more forks.
I doubt it will be "on nearly every block". As I explained, if it comes to that, miners will choose a larger weight which decreases their invalid rate.
I didn't talk yet about how to handle transaction fees, so you may want to defer judgement until then. Hint: You won't be able to get the entire fee of all floating transactions by creating a very light block.