Rolling the lawn compacts the soil, making it more difficult for the turf grass roots to penetrate into the soil. Soil compaction makes it harder for the grass to grow and thus easier for the weeds to compete. The only thing that rolling does well is to flatten out any bumps in the lawn. Mind you, a stiff raking will accomplish the same thing. Lose the lawn roller.
Turf grass thrives on the same kind of soil found in gardens.
Rich or fertile, well drained loam is best and soils that are high in organic matter tend to grow the best grass. In our modern world, we can add organic matter by spreading peat moss and compost on our lawns. My working recipe calls for one bale of peat and two 30 litre bags of compost for every 1000 square feet of lawn. It also helps to add some grass seed every year to thicken up the lawn. A thick lawn fights off weeds better than thin stands of turf.