  We look at some extensions of the Stieltjes-Wigert weight functions. First we
replace the variable x by x^2 in a family of weight functions given by Askey in
1989 and we show that the recurrence coefficients of the corresponding
orthogonal polynomials can be expressed in terms of a solution of the
q-discrete Painlev\'e III equation. Next we consider the q-Laguerre or
generalized Stieltjes-Wigert weight functions with a quadratic transformation
and derive recursive equations for the recurrence coefficients of the
orthogonal polynomials. These turn out to be related to the q-discrete
Painlev\'e V equation. Finally we also consider the little q-Laguerre weight
with a quadratic transformation and show that the recurrence coefficients of
the orthogonal polynomials are again related to q-discrete Painlev\'e V.
