Awesome! Thanks for the further pointers. After analyzing your formula it led me to the following:

=lookup(randbetween(1,sum(B2:B6)),C2:C6,A2:A6)

column C has a running sum of B, i.e. C2=sum(0,B2), C3=sum(C2,B3), etc.

In my formula column B is the weighted values, column A is the values, column C is the running total of B