Cycling times will vary but at week 2-3, you are in essence completing your cycle for introduction of fish.
The purpose of a cycle is to create bacteria that will be consuming ammonia and nitrite from your livestock, but you have to get the bacteria from somewhere initially. Why is it called a cycle? Because the tank will go through three phases: ammonia will rise and fall, then nitrite will rise and fall even quicker,( although dont occupy yourself with nitrite in a marine tank unless sky high) and lastly nitrate will rise and fall. Once Ammonia reads 0 and Nitrate is less than 20ppm, the cycle is complete and livestock can gradually be introduced. The bacteria population will increase with the new bioload, processing waste and converting it to nitrate rapidly. However, it is important to note that overloading the aquarium with too many fish initially can exceed what the bacteria can handle. This is why it is best to add new fish slowly over the next few months. The bacterial levels will adapt if you don't overload the system with too many mouths to feed.
What copper product are you using for Qt ? What test kit are you using to monitor copper level?