My advice is if you're interested in copper do 2.5-3mm or go to Aluminum. Copper has a much faster heat transfer than Aluminum but it also loses heat faster which isn't desirable if you want to cook anything. So to make a long story short if the copper is too thin it's worthless. You can imagine cooking in a thin aluminum camp pan.... put the food in, pan goes cold. In my opinion 3mm copper is superior to aluminum but 2mm is not. There's really no way around the heft while keeping the advantages of copper. If the pan is too thin it will heat up fast and cool too fast.
The Cuprinox Pro line like these Mauviel Cuprinox Pro 2.5mm
I will repeat though that it's worth it to get them from Paris. The store at the link wants $359 for the 11" fry pan, I paid $145. The 9.5 inch lid is $105, I paid $40. It's worth the trouble to have it shipped.
My original plan was to use copper only for my frypans where searing was really important. On a whim I bought a 9.5" copper sauce pan too and suddenly I could cook the best risotto I've ever had. It browns onions perfectly, transfers to the oven, makes risotto etc.. It was a wonderful thing so now I have a 4.8", 5.5", 7" and the 9.5". I also bought a 10 inch fry pan and an 11.6". The 10" never gets used because it's too small so the last time I was in Paris I picked up another 11.6 and now I'm happy. I bought a 9.5 inch saute pan and it too never gets used. Both the fry pan and the saute pan will end up on ebay as soon as I get the them polished.
You don't use one material for all of your pans either. I have eight copper frypans/sauce pans, two enameled cast iron dutch ovens, two seasoned cast iron comals, 1 each seasoned cast iron fry pan and grill, 2 All Clad double boilers, 1 All Clad small sautee, 1 All Clad small fry pan, several Wearever non-stick alluminum fry pans and sautee pans. So I have a mix of copper, enameled cast iron, seasoned cast iron, Clad Alluminum, Clad Alluminum/copper and all alluminum and I use them all for different things. They're all the best at what they do. Overall I've ended up with more copper than anything out of trial and error.