First of all, as to needed accuracy, you might be surprised. Jeff Cooper once said that 2 MOA or even 2.5 MOA is accurate enough for a hunting rifle. Think of it this way. Your shot will only be off about 1/4 of the group size. With 2.5 MOA, you are good to over 300 yds.
Second, something is wrong here. That rifle should shoot alot better than that. What I've found is that even the best made light rifles, with ammo they don't like, can easily shoot 3 MOA or more. With ammo they like, they shoot well under MOA.
But, to answer your question, when is a rifle too light ? For me, it's when I can't keep my shots, at least five, in a 10 inch pie plate at 300 yds. from a sitting position. E