Inquiring minds. The anchor part makes no sense.
The anchor part makes sense if he was concerned he might not get the job done with the shotgun. The anchor would take care of a near miss.
It does to me, throw the light anchor over board as to weight yourself down so nobody will find you. If nobody finds you, your family collects insurance. If you wanted to be seen and make a bid hoodoo about the whole thing, you would not be doing it out on the water away from everyone.
You shoot yourself in a way that throws you overboard or in the water treading water next to the boat. The anchor is not enough weight so you can not do this for a minute or so. Some anchors are quite light and in the boyancy of water, easy enough to keep afloat for the length of time needed.
Just my two cents... on a very morbid subject