Pictures did not show up. I do not think you will be able to stop or decrease the flex at all as it is a product of the steel tube itself, filling it will not help.

Either set them deeper into the ground or into a bigger mass of concrete. Deeper will accomplish more with less concrete, assuming it's not the posts themselves that are bending-- you need to inspect closely to see where the flax is. If the posts are bending filling them with concrete will make them much more rigid, but it indicates they were undersized for the task. Dropping a close fitting larger pipe over the existing pipe will also stiffen the pipe.

On farm gates and such that are cantilevered way out the common solution is to add a support wheel to hold up the far end. (Google "gate wheel")

In hindsight scedule 80 2" nominal pipe is 2 3/8 od and 3x as strong as fence pipe. The assembly would be much stiffer had you spread pipes wider and put struts between. If you can spare space sink a scedule 80 pipe 12" away and install struts to create a web truss. A brace across top from end to end will help.