  Affine structures on a Lie groupoid, including affine $k$-vector fields,
$k$-forms and $(p,q)$-tensors are studied. We show that the space of affine
structures is a 2-vector space over the space of multiplicative structures.
Moreover, the space of affine multivector fields has a natural graded strict
Lie 2-algebra structure and affine (1,1)-tensors constitute a strict monoidal
category. Such higher structures can be seen as the categorification of
multiplicative structures on a Lie groupoid.
