Does modifying the grades multiple times make me look unprepared/unprofessional? As a TA, I have to grade students' assignments.
The main instructor usually has requirements regarding the minimum average grade for the class.
At the same time, it is tricky to predict the class' performance until I have graded about one third of the students' papers (for larger classes, and one half for smaller classes).

Even then, unexpected things can come up. To ensure fairness as well as fulfill the minimum average grade required by the instructor, I often have to re-grade their papers multiple times. For example, when first grading Josh's work, I gave him 4/5 pts for question 1. After finding out some others did better than him (but still not entirely correct), I gave the other students 4/5 and take one more point from Josh, and this process keeps going on and on. As a result, when I return the assignments to the class, their papers are full of my corrections for their previously assigned points.

I did mention curving to the instructor, but he didn't seem to be OK with that. In fact, he manually re-graded the first HW instead of curving it, which made me feel bad (and insulted).
It doesn't seem like the students have an issue with the way I grade, but I still wonder whether modifying the grades multiple times make me look unprepared/unprofessional?*
Modifying the grades consumes extra time and effort in addition to that required by the grading itself, so regardless of professionality, you should try to avoid it. I assume that you have all (or large number) of assignments to grade available at once.

Your problem is that you start to grade to early.

First, read all the answers, mark mistakes, write comments, or whatever the standard procedure is. Do not assign any points except full points or no points, and those only in the situation where you are certain that that will be the final score. (Empty answer, total nonsense, perfect answer.)

You'll have to do this anyway, so it does not slow the process of grading. It gives you a good sense of the answers of the students, and so makes it easier to come up with the grading scheme (rubric, I guess, is the jargon here).

The next step is to write your grading scheme. Be as precise as you can, considering the successes and mistakes of the students. Ideally, this should so accurate that the actually grading would be merely comparing the assignment with the grading scheme, but this never happens in practice.

Before you start to grade, check a number of papers and which grades they would get. Check that this is appropriate. If yes, then grade the papers. If no, then revise your scheme and retry.