Clarification of the situation: 1) My wife and two of the children flying are UA premiers (silver); 2) There are four ticketed passengers all upgraded to F (domestic) and C (international) on H fare (two adults and two child tickets) with only ONE CHECK-IN BAG; 3) she was told it was not overweight or excess baggage, rather, it is a per bag overweight situation. We knew before that the limit was 70 pounds, that's why she packed at only 62 pounds.

I just call Customer Relations and they apologized profoundly and promised to look into it.