They carry the same weight as any others that can talk about the candidate's character, work ethic, technical capacity, etc. If one is submitting a recommendation because they know a Col or a FOGO, but they have no clue about the candidate (and I mean can't talk specifics about them) or what is submitted doesn't provide anything "new" to admissions, then it pretty much goes in the garbage. Admissions can read right through the lines and it doesn't look good if the only reason for submitting the letter is because of the submitter's rank. This was a briefing point at our BGO summer training.
Now, if the person can provide something that is unique, new, not covered in the application (which includes the teacher's recommendations) and happens to be a Col or FOGO, then no issue...it might bring some credibility to the recommendation, but probably nothing beyond that.
So if you are submitting an "extra" LOR, I would make sure that it doesn't repeat something in the application/record.
** Edit: Depending on HOW the record is briefed, the individual's name might not even be mentioned to the board...so they might not even know who the LOR is from.