Maximum weighted disjoint set union
This is a weighted version of Set Packing, which was one of the 21 classic problems proven NP-hard by Richard Karp:


  Richard M. Karp (1972). "Reducibility Among Combinatorial Problems"
  (PDF). In
  R. E. Miller and J. W. Thatcher (editors). Complexity of Computer
  Computations. New York: Plenum. pp. 85–103.


As the unweighted version is already NP-hard, your weighted version is too, so it's unlikely that any algorithm will solve every instance of it in polynomial time.