Hi Cindy
In your sentence, solid refers to the quality of the food, not the fact that it does not change much, and to expand on, rather than emphasise, the unchanging nature of the diet. Here, solid is 'mundane' or 'stodgy'; meat and potatoes weighing heavily on the stomach compared to, say, salad, fruit or a more varied diet.
Without further context or evidence this appears to be a somewhat sweeping generalisation - it might be true, but I have never heard of the American diet referred to in this way.