Complex sorting in mysql
===

I have a table 

    user problem problem_weight running_time
and i want to sort **users** 

first according to **aggregate** of **problem_weight** and then
 
if a clash occurs according to **minimum running_time** of a **problem having maximum weight**, 

if it still doesn't resolve then acc. to **running_times** of subsequent **problem_weights**

I am able to do the first part by

    SELECT user, SUM(problem_weight) AS weight
    FROM myTable
    GROUP BY user
    ORDER BY weight

but how to proceed after that?