  We consider bounded weight modules for the universal central extension
${\mathfrak{sl}}_2(J)$ of the Tits-Kantor-Koecher algebra of a unital Jordan
algebra $J$. Universal objects called Weyl modules are introduced and studied,
and a combinatorial dominance criterion is given for analogues of highest
weights.
  Specializing $J$ to the free Jordan algebra $J(r)$ of rank $r$, the category
$\mathcal{C}^{fin}$ of finite-dimensional $\mathbb{Z}$-graded
${\mathfrak{sl}}_2(J)$-modules shares many properties with the representation
theory of algebraic groups. Using a deep result of Zelmanov, we show that this
subcategory admits Weyl modules. By analogy, we conjecture that
$\mathcal{C}^{fin}$ is a highest weight category. The resulting homological
properties would then imply cohomological vanishing results previously
conjectured as a way of determining graded dimensions of free Jordan algebras.
