How do I stop it? I'm not daydreaming, I just enter this state where I can still see everything around me, but I don't 'register' it. I could be just hanging out with friends having a good time, in class or just sitting on my bed - when I suddenly space out. I tend to feel quite weak when this happens too and have zero motivation to do anything. My therapist (for my depression and anxiety) says it could be my brain telling me to take a break, but this happens to me when I'm resting as well, so that doesn't really make sense... Help please.

Have you been tested for or diagnosed with Attention Deficit disorder? It also could be from over stimulation all day every day and your brain begs for some quiet time. Beyond just sleeping. This one I understand all too well being on the go consistently 16-17 hours a day every day.

TV isn't quiet time...Listening to your IPOD isn't quiet time...Texting friends isn't nor is surfing the internet.

At most.....try reading a book in a quiet room a couple hours a day...no tv on no music playing...just focusing on ONE thing without half a dozen others going on.

Sounds like depression in some respects... speaking as someone who has had plenty of it over decades.
A fancy psych term might be 'dissociation,' but that just means what you said - spacing out.
Plus (I don't want to enter into territory that is between you and your doctor or doctors), your body could be trying to adjust to different types of drugs that maybe don't work well together, such as antidepressant with anti anxiety, IF you take any.

Teens and early 20s are very very often a time of anxiety, depression, and a thousand thoughts tumbling around in our brains all at once. I coped by reading existentialist authors and saying I was disaffected, dropping out of college, not wanting possessions or a home, drifting around political unrest... but I was really just depressed. It has taken me 50 more years to drop all the terms and labels and diagnoses.

Get a full blood panel to see if you are nutritionally deficient in anything - thyroid, iron, B vitamins, magnesium.. all sorts of ways to get weak and depressed that are more physical than mental.
Eat a healthy diet! I know I didn't as soon as I left home.

Your thread has been moved to a Medical Board since your question is not relationship related.

How old are you? Have you talked to a doctor (other than your therapist) and have any tests been preformed?