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Can anyone please explain to me why deflection/strain gauges couldn't be used on aircraft landing gear struts to provide an instant and true reading if the aircraft's weight, and by relative readings, balance? It seems to me that this would be more accurate than calculating those factors using averages, and would remove the human error factor.

In the case of GA airplanes, especially those with propellers, MONEY. The sensors, computer and associated wiring would all cost money and require certification (more money) and add to empty weight. The old tried and true WxA=M with a calculator can now be replaced with computer programs for a computer or IPAD Apps. Also money but much less. All that is possible is not practical. And for a real nitpicker the numbers need not be averages. With all the respective weights and stations the gross weight and C.G will be quite accurate. Popular Science might say this is coming but if you ask Beech, Cessna, or Piper they would say not likely any time soon.

This 5 year old study ( www.skybrary.aero/bookshelf/books/1149.pdf ) concludes that such systems might not provide the accuracy needed. I agree that for GA the cost of the system would be prohibitive. However, for Commercial, Cargo and Business aircraft costing from $1 to 10's of millions, the cost sould be more manageable. The referenced study above used 1700 W&B incidents in the past 40 years. The cost of destroyed aircraft is massive; the cost of human lives in incalculable. I'm sure that a dedicated research and development program could produce an accurate system.

The system does exist on larger, modern airliners.
For instance, from the Boeing website:

SEATTLE, March 27, 2007 -- The Boeing Company [NYSE: BA] selected Crane Aerospace & Electronics to supply the onboard weight and balance system for its new 777 Freighter, making it the first commercial airplane program to choose the new advanced technology known as AirWeighsTM.

"The ability to quickly provide accurate weight and balance calculations will enhance the efficiency of operations for 777 Freighter customers," said Kim Pastega, engineering integration leader for the 777 Freighter Program, Boeing Commercial Airplanes. "We are pleased to have Crane supply this technology for the 777."

The onboard weight and balance system is designed to provide measurements of the 777 Freighter's weight and center of gravity. Operators benefit from having accurate and reliable weight and balance measurements provided in real time. In addition, the system can quickly validate manual weight calculations.

"This is a significant application of our new weight and balance technology because of the advantages it offers freighter operators," said Greg Ward, Aerospace Group President of Crane Aerospace and Electronics.

The AirWeighsTM system uses an airplane's landing gear struts as scales to determine the load-bearing pressure at each strut to calculate weight and balance measurements.