Regardless of your ticketing/PNR method, it will be up to United whether or not to honor a 70-lb limit. You may get lucky, but I wouldn't count on it.
For domestic travel on United you may check two bags free of charge with a maximum weight per checked bag of 50 pounds/23kg each. United's 1K, Premier Executive and Star Alliance Gold members are allowed a total of three pieces of checked baggage (maximum of 70 pounds/32kg each) free of charge.
According to the SQ website, flights to/from the USA are on the piece concept. For Economy class:
Two pieces, of baggage are allowed. The total dimension (length + width + height) of both pieces must not exceed 273 cm (107 in) and the outside linear dimensions of each bag must not exceed 158 cm (62 in.) The weight of each piece is limited to 32 kg.
KrisFlyer Gold & PPS Club members are entitled to more.
http://www.singaporeair.com/saa/en_U..._allowance.jsp
FWIW, Continental doesn't honor the higher baggage limit, and I had to pay them twice because of my stopover enroute to catch my SQ international connection.
I find this to be one of the more irritating practices of the airline industry.
You might be interested in taking a look at this thread on the same subject:
http://www.flyertalk.com/forum/showthread.php?t=655037