I have an 09 Ram 1500 Quad. There are what appears to be a pair weights hanging from a bracket on the outside of the frame (both sides), about a foot behind the front cab/chassis bolt. Any ideas on what these are for?

 

I think I read somewhere for harmonic balancing?

 

yes, vibration dampers.

 

Vibration Dampers...
Or possibly involved in the "Wheel Shake" / "Body Shake" of this thread:
https://dodgeforum.com/forum/4th-gen...h-gen-ram.html

I got the Shakes... At 65-70mph, I got'em Bad...

 

Take them off and see what happens then.