Student or Learner
"She had heard the weather forecast on the radio and they said it might rain later."
Why is "migt have rained" not used instead? It's an indirect speech, so I suppose there must be a change in the tense, eh?
IMHO, "might" is used from the point of view of the past. From the point of view of the present we should say "it may or might rain."
Same with: "She had seen that movie a lot of times but said she would watch it again."
But let's see what native speakers will say.