In this article, for $N \geq 2, s \in (1,2), p\in (1, \frac{N}{s}), \sigma=s-1 $ and $a \in [0, \frac{N-sp}{2})$, we establish an isometric isomorphism between the higher order fractional weighted Beppo-Levi space
\begin{align*}
{\mathcal D}^{s,p}_a(\mathbb{R}^N) := \overline{C_c^\infty(\mathbb{R}^N)}^{[\cdot]_{s,p,a}} \text{ where } [u]_{s,p,a} := \left( \iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{\left| \nabla u(x) -\nabla u (y) \right|^p}{\left|x-y \right|^{N+\sigma p}}\, \mathrm{d}x\mathrm{d}y \right)^{\frac{1}{p}},
\end{align*}
and higher order fractional weighted homogeneous space
\begin{align*}
\mathring{W}^{s,p}_a(\mathbb{R}^N):= \left\{u \in L_a^{p^*_s}(\mathbb{R}^N): \|\nabla u\|_{L_a^{p^*_{\sigma}}(\mathbb{R}^N)} + [u]_{s,p,a} < \infty \right\}
\end{align*}
with the weighted Lebesgue norm
\begin{align*}
\|u\|_{L_a^{p^*_{\alpha}}(\mathbb{R}^N)}:= \left( \int_{\mathbb{R}^N} \frac{ |u(x)|^{p^*_{\alpha}}}{|x|^{\frac{2ap^*_{\alpha}}{p}}} \, \mathrm{d}x \right)^{\frac{1}{p^*_{\alpha}}}, \text{ where } p^*_{\alpha}=\frac{Np}{N-\alpha p} \text{ for } \alpha= s,\sigma.
\end{align*}
To achieve this, we prove that $\mathcal{C}_c^{\infty}(\mathbb{R}^N)$ is dense in $\mathring{W}^{s,p}_a(\mathbb{R}^N)$ with respect to $[\cdot]_{s,p,a}$, and $[\cdot]_{s,p,a}$ is an equivalent norm on $\mathring{W}^{s,p}_a(\mathbb{R}^N)$. Further, we obtain a finer embedding of ${\mathcal D}^{s,p}_a(\mathbb{R}^N)$ into the Lorentz space $L^{\frac{Np}{N-sp-2a}, p}(\mathbb{R}^N)$, where $L^{\frac{Np}{N-sp-2a}, p}(\mathbb{R}^N) \subsetneq L_a^{p^*_s}(\mathbb{R}^N)$.