I owned an 07 Cobalt 2.2 ecotec. I ran syn 5w-30 according to the oil life monitor (wrong decision for long term performance), which usually ended up being close to 9-10k on OCIs with full syn oil and an M1 or Puro Syn filter. Filter always looked like [censored] at the end of an OCI (partially collapsed and filthy). And, no, this wasn't from install (I checked; the crush was not due to the cap being tightened). Sold it at 130k with some top-end clatter.
For this motor, ST synthetic 5w-30 at 1k intervals with a FU or M1 filter, with some seafoam added to the crankcase for the last 100 miles of each OCI. Do not go thinner. 10w-30 synthetic would be just fine as well.