The reasons to sim your character are: (1) the stat weights included by default with Pawn do not take into account your current stat values; and (2) in some cases the default weights are either stupid or flat out wrong for your build (or even the build they were meant for).

Running simc on your character with your current gear will give you stat weights that indicate, for the talent setup and type of fight you choose, which stats you benefit the most from adding additional points of, so that you can see the actual relative benefit of swapping pieces out, or comparing two possible upgrades to see which is better.

For instance, we all know that some specs highly favor crit, but what if you already have a ton of Crit on your gear?

In that case, running Simc and to generate scaling factors may tell you that, at your current gear setup, you actually gain more from adding a piece that has Mastery or Versatility, because currently your values of those stats are very low, each point gives you much more gain in terms of the percent added per point of rating, and additional points in Crit would give you relatively much less marginal improvement.

So, whereas early on Simc would have told you to favor Crit above all, later, when you already have about all of it you can use, it will tell you to favor other stats that give better marginal improvements.

You don't need to re-sim with every gear change, and it's a waste of time to sim before you get to the level cap and close to whatever ultimate item level range you likely will be gearing to.

So, if you plan to go no farther than heroic raids, for instance, you could start looking at sims when you're getting into the range of say 860+, so that as you begin to collect those raid drops and other high end pieces of gear you will be using for a while, at least until the next raid tier comes out, you can try to choose the best individual pieces available to balance out your stats, and as you get other drops over time you can decide whether any of them are worth swapping out.