How can I add a extra feature to repeating date field? I have a content type named Tasks and it has a date field. 

I use this date field for weekly tasks and I want to add a simple on/off checkbox for these dates.

For example I add a weekly task for 11 November 2016 and I pick repeting option to every week.

I want this;
Field Collection is exactly what you looking for. It allow you to create a group of fields, and then add this group of field as a field on your content-type (and made it repeatable as your date field).

In your case, you create a field collection constituted by a checkbox field, and a date field. Then add this field collection to your Tasks content-type and made it repeatable (Unlimited).