Larger trees grow more slowly due to increasing competition (especially for canopy space) with their neighbors.
If trees are planted with sufficient spacing, an old tree's outer growth rings will be the same density as the inner growth rings. Trees grow to the water, sunlight, and nutrients that are available to them -- up until they become diseased or they grow so large that they struggle to support their own weight (at which point they start losing branches, which means they no longer get enough sunlight). To counteract the pull of gravity, older trees stop gaining height and instead focus on adding girth (i.e., thicker growth rings).
Tree plantations achieve a higher wood output by progressively thinning the plantings as the trees mature. This allows the remaining trees to keep growing at a fast clip and results in more even grain in the lumber.