How to thicken salad dressing

A very small amount of xanthan gum will work. It is commonly used in salad dressings. Be careful though, too much will result in an unpleasant texture that some describe as mucus-like. Maybe start with 1/4 tsp. Wisk in and increase from there as necessary, but in very small amounts. Xanthan takes a while to hydrate and thicken. Start with a small amount, as the thickening power will increase with time. You can always add more later.

Most dressing is thickened by an emulsion, so @moscafj's answer of xanthan gum is probably the most direct improvement of this recipe if you're happy with the flavor balance. But another thing you might consider is looking for real aged balsamic rather than the thinner stuff most people use in salad dressings. Real aged balsamic is much thicker. When my wife and I were trying to learn to make dressing with little or no oil, we found that straight aged balsamic made a good dressing on its own. The down side is that it can be fairly expensive by comparison.

To modify this recipe with true balsamic, you'd want to remove the water. Start with 1/4 cup of the balsamic (much stronger flavor) and add more to taste.

Another thing that works well is to blend the dressing with an avocado. While there's fat in the avocado, it's healthy fat from a whole food. You're also adding much less fat than you would to make a strong emulsion with oil. You may want to start with less/no water in this modification, too, and add it back until you're happy.

Garlic can also add creaminess depending on how you prepare it, but you typically need a little course salt. (Which you said you're trying to avoid, so you'll have to decide if the small amount of salt is worth it)

Basically, you finely crush or mince the garlic and then grind the salt into it until it's a paste. This can be done with a mortar and pestle or simply by using the side of your knife to grind the garlic and salt together on your cutting board.

It's possible that you might be able to avoid the salt if you blended the garlic and lemon juice in a blender, but I've never tried it. (I don't know how if the salt is just for abrasion, nor if acid would cause problems)

If the salt is only needed for the abrasion, you might be able to use the black pepper or crushed mustard seeds in place of the salt

I understand your plight when it comes to homemade low fat salad dressing. I also use a low fat version, but not as little as a few tablespoons of oil. The problem I find going that low on oil is the need to sweeten the vinegar for it to be palatable. All that straight vinegar is hard on the throat, which is why I'm assuming you add the water. I may be repeating some of the advise already given, but it will be in a different context.

Instead of water, may I suggest adding 1 to 3 teaspoons of honey. Not only will it sweeten and smooth out the vinegar taste, it will also help to thicken the dressing. An alternative option is a Balsamic reduction. Now I know what you thinking, it will only be stronger. However, reducing "Balsamic", will actually sweeten and thicken it. Using the higher amount of honey, you can try using other vinegars, but make sure it is a really good brand. Treat it like wine. The better the brand, the smoother the taste. Try white wine vinegar with the honey. Also try replacing 25% to 50% of the vinegar with tangerine juice and a tsp of it's rind.

Lastly, you generally use less dressing when it's low fat which can make it harder to distribute. I always put the dressing in the bottom of the bowl first, then add cut tomatoes in next and all other veggies on top. The juice from the tomatoes adds to the dressing. Toss well by going down the sides of the bowl, then pull to the center and pick up. Believe it or not, it is a technique that works. I hope this helps.

A little bit of ground flax or chia seed can thicken it, but much like xanthan gum, too much can make the texture unpleasant. I'd mix it with the water portion and let it sit for a few minutes and then add as much as you need. I do use avocado when I make healthy dressings.