Connecting 4 load cells in parallel
I have also found many documents related to Junction Box or Summing Box for load cells that state that connecting the bridges in parallel is the way for averaging the signals, but I found no one that provided an explanation of the working principle for this. 

Motivated by what Phil G pointed about using Thevenin equivalent circuit and as I found some authors that also suggest the same as this link, I decided to follow the suggested path for the following full-bridge circuit:



First find the Thevenin equivalent circuit as seen from Sig+ and Sig-



Applying the following simplification: ∆R &lt;&lt; R ⇒ RTH ≈ R as in this Application report

When connecting the equivalent circuits in parallel we can solve and find the equivalent output voltage



As a final result we have that Vout=Vext*(ΔR1+ΔR2+ΔR3)/(3*R), which reflects the relationship between the output and the average of the ΔRs from all the bridges.