The filing by the former Massachusetts governor came on the same day as the House began public impeachment hearings of Trump in Washington.
Weld says if Trump were to be reelected, "I think that would be a tragedy for the country."
Mark Sanford, the former South Carolina governor and congressman, dropped out of the Republican primary race on Tuesday, leaving Weld and former Illinois Rep. Joe Walsh as the remaining major Trump primary challengers.
Walsh is scheduled to file for the first-in-the-nation presidential primary Thursday.
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