Advice on trust issues

So I went away a couple weeks ago to visit family. My husband stayed home because of work and our dogs. One night I fell asleep super early around 8 pm. He texted me saying “hey do you mind if I go out with my buddies tonight?” I didn’t answer. I woke up at 1 am and tried to call him about five times, he didn’t answer so I figured he had gone to sleep. At 3 am he texted me “No babe I didn’t go out, I fell asleep shortly after you did”

Okay, so I come home and I ask him about it again and he straight up says “No, I promise I didn’t go out.” Something just didn’t feel right about it.

A week later I was using his phone and “stumbled”, yes I was snooping and that’s messed up, upon a message to one buddy saying “just walked in”. When I confronted him once again he boldface lied to me. After a few minutes he finally cracked and apologized saying he did go out blah blah.

Now, I’m insecure and he knows this. I’m working on it, but in all my life o have never placed my full trust in any man I’ve been in a relationship with until now. I feel betrayed that he could keep up a lie like this with me (he’s an awful liar in most instances).

I guess the advice I’m looking for is, how can I stop perseverating on this and allow myself to fully trust him again. It’s not so much WHAT he lied about, but the fact that he did over something so dumb!

I know, I’m overreacting I just want to know how some of you ladies would feel