Try shooting lots of WD40 into the shifters. Friction builds often builds up in STI shifters due to hardening of the original factory grease and also from dirty water spray from riding in wet conditions.

Both Shimano and Campagnolo recommend greasing cables when installed. I doubt that additional lubrication will hurt them. Dirty water spray can certainly add to friction inside the housing, especially the short housing found at the rear derailleur. Shift to the smallest cog and see if you can release the short housing and slide it forward on the cable, exposing it so that it can be lubed. It may be necessary to release the cable from the rear derailleur. If this is done be sure to re-attach the cable exactly as it was before releasing it. If lubing helps shifting performance consider it a temporary fix and plan to replace the cables and housings soon.