1/2 mile visibility isn't all that bad. Is the aircraft Cat-II or Cat-III autoland certified? It might be a good time to return to the departure airport. If you were taking off below landing minimums, I can't really figure out why the takeoff alternate is below mins.
But I certainly wouldn't entertain a "below minimums" approach because of a single passenger. Now if we're all about to die, that's a little different, but you really don't want to risk killing 149 (at least on the -88) passenger for one passenger that might have a case of gas (no doctor onboard).
If the weather is all screwed up at your destination, chances are any nearby diversionary airports are too... *IF* you've got charts for the offline (not normally served by your airline) diversionary airport that's at or above minimums.
But that's just one guy's opinion!
