The tortoise and the hare

Hey there people. Ready to give me your advice? Great - because I need it. Background: 9 weeks ago I (female in her 40s, no kids) / him (met a male in his 40s, 2 kids) online. We vibed, and agreed to meet up the following weekend.

Fast forward, everything went great. We speak daily and we see each other every other weekend. He attempts to spend the night each time. I decided to drive to where he lives and he attempted to have me spend the night there. He has about a 50% success rate.

He speaks about us in the long term future and.... I'm still "I just met you and am trying to decide how I feel about you".

This weekend he's already invited himself to stay at my house for three days. When I pointed out that I had plans for one of those days already, he said "I'll just catch up on my show while you're gone". He also was offended that I threw away the toothbrush he used while he was here last.

I don't know how I feel about this pacing. It's amazing to have a guy clear and focused on our relationship development but is it normal to leave a person you just met. 2 months ago at your home alone? I also feel a bit violated because he's already admitted to going through my closets and cabinets and I just feel that doing that is a red flag for something - what exactly I'm unsure. (Is that normal)?

Am I moving too slow/ the abnormal one?