Loosley, a Courant algebroid is a vector bundle with a Loday-Leibniz
bracket and a nondegenerate bilinear form on its space of sections
together with some compatibility conditions. Following Roytenburg it is
known that Courant algebroids have a neat supermanifold formulation as
'symplectic Lie 2-algebroids'. Without details, we have a graded
symplectic supermanifold and an odd Hamiltonian that is homological,
i.e., $\{\theta, \theta\} =0$. In this talk, I will show how pre-Courant
algebroids, so 'Courant algebroids' without the Jacobi identity, have a
very similar formulation as 'symplectic almost Lie 2-algebroids'. In
particular we condition on the odd Hamiltonian is relaxed to be
$\{\{\theta, \theta\},f\} =0$ for weight/degree zero functions. We will
explore some of the consequences of this reformulation, including how to
describe pre-Courant algebroids with an additional compatible
non-negative grading. Examples of what we refer to as weighted
pre-Courant algebroids include Courant algebroids in the category of
vector bundles. As a side remark, Courant algebroids and their relatives
have made a resurgence in theoretical physics via double field
theory. Based on Andrew James Bruce & Janusz Grabowski, *Pre-Courant
algebroids*, Journal of Geometry and Physics 142 (2019) 254-273.