  Let $\mathcal G$ be a stratified Lie group and $\{\X_j\}_{1 \leq j \leq n}$ a
basis for the left-invariant vector fields of degree one on $\mathcal G$. Let
$\Delta = \sum_{j = 1}^n \X_j^2 $ be the sub-Laplacian on $\mathcal G$ and the
$j^{\mathrm{th}}$ Riesz transform on $\mathcal G$ is defined by $R_j:= \X_j
(-\Delta)^{-\frac{1}{2}}$,
  $1 \leq j \leq n$. In this paper we give a new version of the lower bound of
the kernels of Riesz transform $R_j$ and then establish the Bloom-type two
weight estimates as well as a number of endpoint characterisations for the
commutators of the Riesz transforms and BMO functions, including the
$L\log^+L(\mathcal G)$ to weak $L^1(\mathcal G)$, $H^1(\mathcal G)$ to
$L^1(\mathcal G)$ and $L^\infty(\mathcal G)$ to BMO$(\mathcal G)$. Moreover, we
also study the behaviour of the Riesz transform kernel on a special case of
stratified Lie group: the Heisenberg group, and then we obtain the weak type
$(1,1)$ characterisations for the Riesz commutators.
