I think it might be in the contract that he signed that he has to keep on filming (stop/ delay filming = you don't get paid for the entire series).
And no, 4 weeks is no WAY not enough time to grieve especially as they seemed pretty damn close. (and it seems he has a lot of his family on the pay role so maybe he has to keep going to keep the cash coming in?)
I partly agree with you Bobcat.. But surely those who film him ( his own management team) would know better than anyone how he is dealing with his loss and would take the view to delay for peters well being.