TRACON Controller reported loss of separation between two arrivals; indicating he thought it wouldn't work but kept hoping it would.

Narrative

I was working only 2 arrivals. I vectored the second aircraft behind the first to follow inbound on the approach. The vector was tight and I knew it but thought it would work because I kept the first aircraft fast. The first aircraft slowed and the second was too high to slow and descend. For some reason; I thought the weather was better then it was and thought the second aircraft would see the first and I could get an 'S' turn out of him and thought also that the tower would be able to see him. In my mind; I didn't want to take the second aircraft off the approach and make him spend more time in the air and have to waste gas. I was tired and kept thinking the two aircraft would pull away from each other. I switched them to the Tower thinking the Tower could see the two; when I looked up at the weather and knew....that was impossible. I knew from the first vector that I was going to have to make it work....but in the back of my mind I kept thinking it was going to work because I thought the weather was better then it was. As a last resort; I sent the aircraft to the Tower hoping they would 'fix' it. Bad move. I knew in the back of my mind it wasn't going to. Just stupid all the way around; I was tired and not thinking. It's the thought that is in your head when you first do something that may not work. Always act on that thought. It can't be taught; and I know better; I was just tired and hoping it would work.