  We study the weights of eigenvectors of the Johnson graphs $J(n,w)$. For any
$i \in \{1,\ldots,w\}$ and sufficiently large $n, n\geq n(i,w)$ we show that an
eigenvector of $J(n,w)$ with the eigenvalue $\lambda_i=(n-w-i)(w-i)-i$ has at
least $2^i(^{n-2i}_{w-i})$ nonzeros and obtain a characterization of
eigenvectors that attain the bound.
