Empirically I trust that this must have worked, but I'm curious why good fertilizing is often suggested as a way to promote turfgrass growth to crowd out weeds. Why don't weeds benefit from the fertilizer?
Why don't weeds benefit from the fertilizer?
They could, depending on the weed. But the grass benefits more.
Most weeds are opportunistic. They germinate and flourish where the grass is thin or absent. If one keeps the grass healthy, which includes watering, fertilizing, and not cutting it too short, the grass will fill in and shade weeds and their seeds, minimizing their spread.
I'll note that even in a healthy lawn, it's impossible to ensure against weeds 100%. But when the lawn is in good shape, it's very easy to keep up with the weeds, pulling them as needed.