No no no, not weekly, and if you use Cam Guard it also provides a better adhering barrier film. When I store an engine for more than a couple of months I'll pour in a bottle or two (depending on total capacity, I try for 4:1 with good oil and Cam Guard) of Lucas Oil Treatment because it provides a serious adhesive film. I'll start the engine as lean as possible, run it up a bit to get the oil splashed around real good and shut her down. When I bring the engine out of storage I'll run it up until warm to get any dried, oxidized film rinsed back off the surface and change the oil.
I'll give you the benefit of what Ed Collins, maker of Cam Guard and former petrochemical engineer for Exxon who was tasked and funded by them to develop the best Aviation oil (then rejected it as not cost effective and just copied Aeroshell 20-50s Semi Synth oil which is junk) possible gave me.
His recommendation is to use any of the straight weight oils, or if you want a multi viscosity oil to only use Phillips XC 20-50 (what I use) and dose it with Cam Guard. Ed is available through this board, and if you ever want to talk with him, he has a wealth of knowledge that he will freely share. In fact, he called me one day over a thread because 'It's easier to explain it on the phone', that call lasted 2 hours and was extremely interesting, I wish I would have recorded it for a Podcast because I think everyone should have the base that he so generously gave me. Yes, he is selling a product, but it's a good product with millions of dollars of scientific research and testing behind it.