Talking about paying rent after two weeks gives the impression you can stay for more than two weeks! It can already be seen in the reaction from your friend:
He said he would pay a respectable rent although I am unsure of his definition of respectable.
In other words, he's okay with staying for more than two weeks now, and thinks you'd be okay with that ...
Both of my children have taken in friends with nowhere to live and yes, faced the issue of how to limit that stay. I think the key is in the way you tell the person they can stay. Compare:
Sure, this house is huge, I'll take you in for a while, no problem!
I'm sure you can find a place in the next 6 months, but of course if it ends up that you need a ...
I want to summarise your question slightly differently than written.
You have a house and like your own space.
Your friend has been given 6 months notice to leave his place, is struggling to find a new place, and wants to "move in" (not the same as staying temporarily); you think he may be taking advantage of the situation.
You have told him he ...
"My gut feeling"
Don't ignore a gut feeling. I've done this a couple of times in my life with disastrous results.
If you have someone living with you because of your feelings of guilt, you will inevitably build up resentment. This will finish your friendship. You will end up arguing about shared food, who cleans the bathroom, who pays for what and ...