By default Apticron runs once a day. To only get email notifications once a week, delete the daily cron job:
Then edit /etc/cron.d/apticron, it will look something like this
51 18 * * * root test -x /usr/sbin/apticron && /usr/sbin/apticron --cron
The last star sets the day on which apticron will run (a star means everyday). Change it to a number to set the day of week (0 – 6) it should run, where 0 is Sunday. E.g.
51 18 * * 0 root test -x /usr/sbin/apticron && /usr/sbin/apticron --cron
to have it run once a week, on Sundays at 18:51