Can a thicker chain cause it to slide/jump under pressure? I recently changed my chain on my roadbike. It's a roadbike made to a single speed.

Anyways, the new chain is a bit thicker than normal. I applied the same number of chain links to the new chain. After switching the chain, the chain jumps/slides under pressure. A problem I had before because the chain wasn't tight enough.

This time i can't figure out why the chain jumps. It looks tight enough. Could it be the width of the chain?
No. Most common chains are 1\8 (single speeds) and 2/32 for your average multispeed chain. Of course 8 and 9 speed chains can be thinner.  It may be your sprocket. You didn't state how many miles is on the bike in it's current setup. If the rear sprocket is worn, chain will skip.

Also if the chain alignment is too far off, it will skip or come off. A single speed set up puts more load on a chain without a derailleur to dampen some of it and hold it in place.

A bent chainring on a crank can possibly throw it off or cause similar problems.

If you just shortened your chain and pieced it back together by driving the pin back between the links versus using a or the masterlink, that point can be too tight and inflexable depending on how far the pin was pushed in. It can be microns of a difference and that link won't flex.