Hmmm... Well, I believe its never too late to switch to the right engine oil grade / viscosity (especially while shifting from unnecessarily, extremely thick engine oil to thin oil, like 20w-50 Vs 5w-30, and mineral Vs Fully Synthetic), and also provided that engine and its seals are fine (I already mentioned it, otherwise, if engine is weak and seals might become leaky, then thin oil may not be recommended).
I think, Corolla 1.6L, 2013 model has 1ZR-FE engine, and for that; 0W-20, 5W-20, 5W-30 and 10W-30 are the recommended oil grades (Source: http://mywikimotors.com/toyota-1zr/ ). 10w-30 is the max. here (and is also the max. thickest oil grade I have found in most of the recent Toyota engines), but is the thickest.
Still, experts can guide better 