Multpile sets of rules in altium (Rules by selected area)
Create a 'Net class' called something like 'Power' and make a rule that applies to nets in that class only, then add the heavy current nets to that class. 

You can also do things like add rules to change clearances and polygon connect styles to such a class which can be useful.

Altium is very much rule driven design, it pays off bigtime to learn the intricacies of the netclass and component class systems.