In this paper, we establish some conditions on nonnegative rd-continuous weight functions $$u\left( x\right) $$ and $$\upsilon \left( x\right) $$ which ensure that a reverse dynamic inequality of the form $$\begin{aligned} \left( \int _{a}^{\infty }f^{p}(x)\upsilon \left( x\right) \Delta x\right) ^{ \frac{1}{p}}\le C\left( \int _{a}^{\infty }u\left( x\right) \left( \int _{a}^{\sigma \left( x\right) }\mathcal {K}\left( \sigma \left( x\right) ,\sigma \left( y\right) \right) f(y)\Delta y\right) ^{q}\Delta x\right) ^{ \frac{1}{q}}, \end{aligned}$$ holds when $$q\le p<0$$ and $$0<q\le p<1.$$ Corresponding dual results are also obtained. In particular, we prove some reverse dynamic weighted Hardy-type inequalities with kernels on time scales which as special cases contain some generalizations of integral and discrete inequalities due to Beesack and Heinig.