Yes, such a [system exists][1]. It was [developed during the sixties][2] and installed as an option on the Boeing 707-300 freight aircraft. Other aircraft that had a similar (optional) system include the Concorde, L1011 and Boeing 747.  

It is mostly found on freight aircraft because they have a less predictable load distribution (centre of gravity) than passenger aircraft. 


 
  [1]: http://aerospace.honeywell.com/products/navigation-systems/sensors-and-inertial-products/weight-and-balance "Honeywell W&B for the B747F"
 [2]: http://www.sawe.org/papers/0626