 Solution

A word of $\mathrm{RM}(d,1)$ is the evaluation of an affine Boolean functionIf $a=0$, the two constants have weights $0$ and $2^d$. If $a\ne 0$, choose $v$ with $a\cdot v=1$. Translation $x\mapsto x+v$ pairs every input where $f=0$ with one where $f=1$. Hence every one of the other codewords has weight $2^{d-1}$.