The National Electrical Code in the US states that any additional ground rods must be bonded together and to the house main electrical entry point with no less than 6ga copper wire and if the run is over a certain length which I forget, it needs to be even bigger.
So, if your smaller than 6ga on your ground rods you are not to code and you should upsize. If you have not bonded new ground rods to your house main electrical entry point you should do it. See NEC Article 810.
Would there be any advantage to running heavier battery cable type jumpers between my ground rods ?