This is a summary of distances of the main section of Sörmlandsleden 1-62. In the right column you can find distances between places to restock on food. Mostly larger grocery stores in or near cities and villages. There might be cafés, gas stations etc in between.
Do your own research, this is mainly for help in planning. Opening hours might me limiting, shops close up etc.
Section 11-20 looks to be the hardest to find a store or similar. I will update when I know more about those sections.