An arrow with a stiffer spine is not necessarily heavier. Take a 2512 Easton (deflection:.321, weight at 29": 281 grains)and compare it to a 2020 Easton (deflection: .426, weight at 29": 392). There are also heavier carbons out nowwith less spine.

But to answer your question, yes there is a down side to being overspined. What you want is the correct spined (not over or under). What you want is the arrow which shoots through the centershot of a perfectly tuned bow.