Less effort only when the knife moves towards the chopping board, you still have to lift it back up right?
Personally I would think a lighter knife would require less effort in the long run. It might not fall through things by its own weight but surely the difference is marginal if both blades are appropriately sharpened.
Light knife: slightly more effort as the knife moves through food, less effort lifting up for the next slice.
Heavy knife: 'falls through' food easier, more effort to lift up again.
In my opinion in a long prep day the lighter knife wins for me as an all rounder.
However you are referring to home cooking which is different entirely as you don't have to worry about using the knife for a whole day.
I must admit the main basis for why i prefer a lightweight 240 gyuto for most things is that I don't want to be lifting something heavy up and down all day.
Another point although a weak one i must admit ... Brunoise onion surely is not as easy with a 270-300 compared to 240? The further your guiding hand is away from your body the less control you have