How do you know if you are knitting too tightly?
Knitting too tightly
If your yarn breaks you may be knitting too tightly. 
I assume you’re new. I would grab some yarn with the recommended needles and work at it until you come close to the recommended gauge.
I ask because I write extremely hard with a pencil and haven’t done anything in my entire life with a light touch. These leaves me wondering if I knit too tightly, though I make the conscious effort NOT to.
If you grip your needles too tight, it is much harder on your hands. They tire faster & I don’t think it makes the knitting go any faster or smoother. So you are right to try to relax your grip. In the long run, it will be much kinder on your hands.
If you have trouble sliding your sts along the needle or getting the R needle into one to work a stitch, that’s probably too tight. If not, don’t worry about it, and for ‘getting gauge’ you can always go up a needle size, the one used in a pattern is a ‘recommendation’ not a 'have to.
I knit really tight. It bends my skinnier needles, and sometimes it’s difficult to slide stitches from one needle to the next.
Basically, as long as you can move the stitches without bending the needles or putting a blister on any of your fingers, you’re fine. You just have to be able to adjust your needle size so that you can match someone else’s gauge.
I find that I typically hold my needles just a bit too tight, but holding the needles looser does not necessarily change my gauge.
How tight or loose you knit is a personal thing, and there is no such thing as the perfect amount of tension. There is a “good” range… and if you fall outside of that range, well, as long as you can make adjustments… who cares?
If you knit tight, I recommend metal or plastic needles. The wood ones feel nice, but they grip your yarn more and make it harder to slide. Also, metal/plastic needles often have sharper points (in my experience)
People who knit tightly say it’s hard to get the right needle into the stitches sometimes. It’s best of if you try to loosen up, but really, if you’re happy with your knitting and it looks good it doesn’t matter. You just have to adjust for gauge as we all do. 
I used to knit really tight, years and ages ago. I finally had to learn to relax and just knit or my hands and wrists would ache like mad. And, let me tell you, that was no way to use a microscope. I decided on a scarf in Garter Stitch and practiced watching TV while I knit. Because it was the same stitch over and over, you can see where I started to relax and just let it go… I keep it to remind myself.