How are the 16 states aggrieved?
Did you read the filing? All sixteen states claim they will be harmed if Federal money directed to each state under the appropriations passed by Congress is diverted to construction of the border barriers. Specifically mentioned is military construction and drug interdiction funds within each state.
Will this fly? I don't know. "If you don't bet, you can't win."
Nothing in the initial paperwork spells out the amount of pain involved, for each state. I guess that will come out during discovery.