I run aero brake levers too. The Campagnolo carbon ones, if you can find a pair, are probably the lightest at around 210g/pair. But they are insanely expensive if you can find them. I searched long and hard and couldn't find anything better. Non aero levers are much lighter. Not sure why, but modern aero levers seem to have a lot more material in the body of the lever than non aero's.
Due to them all being heavy, and most around the 250-270g/pair weight, I just went with a pair of Cane Creek's compact version for my small hands. I changed that a week ago from Shimano's top of the range BR-600's, which although well built and 10g lighter for the pair, were goddam awfully uncomfortable, and I struggled to reach the levers.
When I get my dremel, I'm going to have a go at lightening the cane creeks. I'll get a couple of pairs of old, well regarded non aero levers, as a comparison for how much potential material I could take out of the body. The levers will also be drilled. Then there is the clamp and clamp bolt to tune as well.
Another option is to go for say a pair of SRAM Red Brifters, and tune them and remove the shifting mechanisms. Weeweenieracer recently tuned his (kept the shifting) and got them down to about 200g with clamps, drilled and sanded levers, and felt hoods. See the thread here: viewtopic.php?f=3&t=107812
I'm guessing the shifting parts would be in the range of 20-50grams total...?
Again, the Red option is insanely expensive unless you can find a set of used levers with a failed mech maybe? Used lever pairs seem to go for at least $200 on ebay...