I think there are several ways that raised beds improve the weed situation. First is that when you build new beds you probably start with soil that is relatively free of weeds and weed seeds. Second the soil people import for raised beds is almost always a lot easier to weed and cultivate than the native soil so it makes removing weeds easier. Third it is easier to reach down to pull weeds in a raised bed so you are more likely to do it often. Fourth the fact that you built raised beds means you are excited about gardening and committed to staying on top of things all summer. Fifth the raised edges make it harder for creeping weeds to get into the beds and make it easier to keep the paths free of weeds. I have had some raised bed gardens that become very weedy with neglect and some at-grade gardens that I kept reasonably weed-free. It is all about continued effort thru the growing season. These days my garden beds are more or less at grade.