"Economy of movement" is something I often hear from teachers and professional players alike. With that in mind, take a full body video of yourself playing, even if it is on a phone camera, and ask yourself "what purpose does this movement serve?" A lot of the movements you will be making are necessary. Your bow needs to move back and forth for sound to happen, your fingers need to move up and down the neck, you likely need to adjust in some way to get to the end of the fingerboard etc. With all of that in mind, look at the movements you are making that are not necessary.
Do you lean forward when playing louder or speeding up? Back when playing softer or slowing down? Do you tap your foot or nod your head to keep tempo? Do the fingers of your left hand move more than a couple millimetres off the string when you aren't using them? When shifting in the lower positions, does your arm move, or your entire body? You should be able to get from half position to almost thumb position without significantly changing much. Mute the recording. Does anything look awkward, weird, out of place, excessive?
Most of the best players I have seen have this all figured out. They make it "look easy" by removing the extra movements that aren't necessary. Principal players will often move a little more than the rest of the section, but a LOT of information can be expressed with a small head nod, a slight lean forward or backwards, or a sideways glance.
You definitely want to be relaxed. Playing while tense leads to all sorts of injuries. I had a professor that said when your section is giving all they have and your conductor still wants more, "the best way to play louder is to look louder." Occasionally you will run into this, or find yourself in an ensemble where theatricality seems to be more important than the music. For the most part, less is more.
Find a balance, but chances are extra movement is doing you more harm than good.
