[nelsb01]

If you have recently replaced the weather striping around the door, be advised that the reproduction material is slightly bigger than the original. And for that reason, doors that used to close properly, are harder to close once the new reproduction material is in place.
Suggestion would be to keep the doors closed and 're-mold' the weather striping using the door pressure against it. This may take some time, but it is easier than messing with door hinges and latches.
Of course, if you did not replace the weather striping ---