This paper is devoted to estimates on weighted $L^q$-norms of the nonstationary 3D Navier-Stokes flow in an exterior domain. By multiplying the Navier-Stokes equation with a well selected vector field, an integral equation is derived, from which, we establish the weighted estimate $∥|x|^αu(t)∥_q ≤ C(1+t^{\frac{α}{2} +ε} )t^{-\frac{3}{2}(1-\frac{1}{q})} ,$$t>0,$ where $ 0<α≤1$ and $\frac{3}{2}<q<∞,$ or $1<α<2$ and $\frac{3}{3−α }<q<∞,$ $0<ε<1$ is arbitrary, and $u_0∈L^3_σ(Ω),$ $|x|^αu_0 ∈L^1(Ω)$ with $∥u_0∥_3$ sufficiently small. With the aid of the representation of the flow, we also prove that if in addition $u_0∈D^{1−1/b,b} _a$  for some $\frac{6}{5} \le a<\frac{3}{2}$ and $1<b<2$ with $\frac{3}{a}+\frac{2}{b} =4,$ then the optimal estimate $∥|x|^αu(t)∥_q≤C(1+t^{\frac{\alpha}{2}})  t^{-\frac{3}{2}(1-\frac{1}{q})},$ $t>0$ holds, where $α>0$ and $1<q<∞.$ Compared with the literature, here no extra restriction is laid on the range of the exponents $α$ and $q.$