Is it compulsory to apply weekly corrections to the ENCs every week or I can wait for update DVD ?

ENCs need to be corrected to the latest notices. The easiest way of doing that is by just inserting the Base cells and update DVD. 

But the issue with that is, these DVDs arrive months after its release. And for these months your ENCs will not be corrected to the latest "notices to mariners".

Now is it absolutely necessary to correct the ENCs or paper chart every week ?

When there were no chartco, Voyager or Digitrace, the notice to mariners used to arrive on board as hard copies. So we used to receive these notices to mariners for last 6 weeks together. And 2nd mate used to have a tough task to finish these as soon as possible.

So do we mean that seafarers were sailing on uncorrected charts and in dangerous way at that time. The answer is NO.

Let us say there was a new wreck discovered close to a port. This need to be communicated to the seafarers working on the ship. How does this information reach ships ? The first information of this wreck would arrive to the ships as EGC navigational warning through Sat-C or through Navtex warnings.

(That makes the Navigational warnings more important than the permanent or T&P corrections).

This nav warning will remain valid for at least 2 months and after that this information is passed as permament correction or T&P correction in the "Notice to mariners".

So if your charts are not corrected for more than two months, you may miss that wreck as this will also not be there as a valid "Navigational warnings".

During those days, even vetting instectors would check if the latest notice is more than two months old. If yes, it would be an observation.

But that was long time back. Now navigation is taken even more seriously. And two months period is no more allowed. Charts need to be corrected every week and that is what is expected by all the third party inspectors and that is the way it should be.

So answering your question directly, Yes.. we need to apply the corrections to ENCs every week. The DVD just acts as the back up and reset point.