The fact that your main post is flexing under load isn’t surprising given how far out the horizontal beam extends. On the up side it tells me the joint between the two is very strong, so, well done with that.
Adding an additional post to your main post (to the side facing or opposite your hammock) would definitely make the design stronger and may be necessary for the structure to survive normal use over time. If you reinforce the main post, it would need to extend under ground to the depth of the current post. Otherwise you are transferring that load to the point where the post is not reinforced and you are likely to see bending there instead.
I have two more two suggestions:
Consider shortening the length of the horizontal beam. This will reduce the force bending your vertical post and also put less strain on your joint. Think about holding a heavy bucket close to your body versus at arms length. At arms length the bucket exerts a more powerful force on you and takes more effort on your part to hold it up.
Also consider adding a brace at a 45 degree angle from the vertical post to the horizontal beam, on the side closest to your hammock. The triangle created is incredibly strong and will make both the vertical post and horizontal beam much more rigid. This is also an old method for creating a rigid structure to hang anything from a sign to a lantern (see the image below).
Take any significant bending/flexing on this structure that supports the weight of a person as a warning sign. Ideally it should be strong enough to survive occasional rough use or even abuse, so I suggest building in a significant safety margin and testing it with a much heavier load, say 400 lbs.
Good luck and whatever you end up doing, let us know how it turns out!
lamp post
