i would first call or go to Discount Tire
ask them if the have a HUNTER ROAD FORCE BALANCE MACHINE
this is Hunters Sales video, but it shows what it can do
It has been almost 40 years since i worked with mounting tires, BUT if i remember correctly
With as much balancing weight as what you mentioned, likely your tire needs to be rotated on the rim
Every tire & rim has a heavy spot, if both heavy spots are close to each other, they would have to put heavy weights 180 degrees away from that point.
You would want the heavy spot on the rim to directly oppose the heavy spot on the tire, then lighter weight can be used