Sometimes you want to track: "What is the size of the largest component?" Since you already maintain a size array for union by size, tracking this is easy.
After each union, check if the new component size exceeds your current maximum. Keep a global maxSize variable.
if union(u, v) succeeded then
maxSize := max(maxSize, size[find(u)])
This pattern appears in problems asking about the largest connected component or when sizes affect the answer.