use date() and mktime():
echo date ("M-d-Y", mktime (0,0,0,1,65,1997));
yes, that's day 65 of january 1997.
and it outputs as
Mar-06-1997
In other words, you could put
echo date ("M-d-Y", mktime (0,0,0,1,($weeks * 7),1997));
to get the date of the first dat of week $week in the year 1997 (or whatever year you want)
Ofcourse you have to take care that the first week starts at day 1, not at day 7.