Best way to overrun the weeds: cut and stimulate the grass to split new roots or grow it high and suffocate the weeds?

So I now have new grass, pretty helthy but with some bold patches
It has reach the point where in some areas is like 4" high nd I can see weeds growing underneath and trying to get access to more light. I have had a long battle with the wild violets, may their species rot in hell :-)) and I am still seeing them popping up here and there. The American weed be gone does not seem to affect them ( I have not been very insistent but a few patches where I run some experiments did not show that they care. Same thing with clover
I was wondering whether I should cut the grass and see where all these things are and go after them or if it is possible to grow the grass that high that they will "suffocate" (no light) and die. I can see that with the grass I have they are week but it is difficult to locate the wild violets and remove them with the grass that way.
I noticed that if I soak the grass well the eeds can be easily removed, it is a relatively small backyard so I can take the challenge but it is still tedious and time consumming