Let me try to approach this from 2 different angles.
I'm a physiotherapist and first I would like to approach this from an anatomical and physiological standpoint.
It sounds to me like you might be lacking some core strength and that resulting in you swaying in your meditation. It could also be that you have some tight muscles around your pelvis and back which is creating muscular imbalances. The balances can cause pulling and tightening in different directions when standing, sitting or lying in certain postures. Muscular imbalances are quite common and not dangerous although if they are allowed to persist over long durations of time they can lead to more serious problems such as limited range of motion, body pain, mal-alignment which again can lead to other diagnoses. Let's not get into this here.
If it's relevant now or becomes relevant you are welcome to contact me on my mail: email@example.com and I will take a look at you either via Skype or you can sent me a video. I will give further instructions about that if you need it.
For now I will give you some strengthening exercises for your lower back and core muscles + some stretching exercises for your hip flexors (m. iliopsoas) since they are often a problem because of too much sitting down. If they are or become tight they can limit range of motion in the spine and external rotation in the hip by creating an increased internal rotation in your upper legs which again will lead to mal-alighment in your spine which will affect your standing, sitting and lying posture.
As you might have heard before the core is our force-generating center. It is very important to have a strong core in almost all activities that one do in ones everyday. A strong core means that one is physically centered. The standing, sitting and lying postures will improve greatly as will many other activities in ones daily life.
The core consists of the following muscles; m. transversus abdominis, m. rectus abdominus, internal/external obliques, lumbal portion of m. erector spinae. Some people count also mm. gluteus, m. quadratus lumborum and m. iliopsas. I will not give exercises for these muscles but only the most important muscles which is m. erector spinae, m. transversus abdominis, m. rectus abdominus and mm. internal/external obliques.
I would like to give you these exercises. They can be a bit difficult to understand when only viewing a photo so I have found this video for you that goes through some of the exercises. I want you to try them all out and find the ones that work best for you. Try to pick 3-4 exercises.
I want you to do 1-3 sets with 10-15 repetitions in each exercise. 1-3 sets meaning that if you have a good day you can do 3 sets and if you are tired or not in the mood you can do 1-2 sets. That way you can regulate it yourself.
You should train these exercises 3-4 times a week. Keep 1 day between sessions for rest.
That was the strengthening exercises now to the stretching exercise for the hip flexor muscles, m. iliopsoas. See this photo. If you cannot do that I want you to do like this instead. You should do 3 sets of 60 seconds on both legs. You can do longer and more sets if you like but this is minimum. This exercise you can do everyday.
If you have any questions feel free to contact me on my mail or write here and I will try to help out.
Now I would like to approach this from a theravada buddhist perspective with basis in vipassana meditation practice.
In vipassana practice we want things to come forth so we can study them. We do not want to interfere with them since that can create attachment or aversion towards the phenomena. By trying to help the swaying or stop the swaying you are really masking/camouflaging the impermanent, unsatisfactory, oppressive and insubstantial nature of the 1st aggregate, the form aggregate.
I believe it's best to just let the swaying be. Observe it. Note it. Observe that you have really no control over the body. The body is oppressive and ungovernable. It is not subject to ones will and by realizing that you can see both impermance, dukkha and not-self.
So in short. Don't interfere with the phenomena. Just observe them diligently and you will come to realize the 3 signs of existence.
As Mahasi Sayadaw has said; "the yogi (the meditator) will come to realize that there is just an object arising and mind arising to that object and no third besides. Third besides is here meaning a self".
Unfortunately I cannot remember where he says that so I cannot quote it.