How many newtons could this BF350-3AA strain gauge support?
Straing gauge do not measure weight, they measure strain (deformation). According to manufacturer's datasheet (http://www.elecrow.com/download/Coding%20System%20of%20Strain%20Gauges-AGS-TECH%20Version.pdf), the BF series can handle strain of up to 2%.

In the scales, the strain gauges are attached to a beam which deforms under weight. The whole assembly is called 'load cell' (sometimes also 'force sensors' and 'load sensors'), and these are rated for specific weight.

Example: http://www.robotshop.com/en/sfe-load-sensor-50kg.html. This one can accurately measure up to 50kg, and can handle up to 150% of that amount (75kg). The website claims it came from bathroom scale.