If someone rents weekly and misses a payment how much notice do you have to give them before you can kick them out?

Where does this person live, they may be considered a lodger

Right, it depends on what state you live in, what your contract says, and whether they live in your living quarters with you (lodger, in some states) or in a separate apartment (tenant). While you are finding this out or telling us, hand him a written, dated, notice to vacate for non payment of rent.

ANY question on law needs to include your general locale as laws vary by area.

Generally, for non payment there is a 3-10 day pay or quit notice. But, also generally, YOU cannot just "kick them out". With rare exceptions, a tenant has to be evicted by court order.