So I know that the fnx uses the "combat" style of sight picture ( the dot where you want it to hit and not the top of the front sight).

I have not shot my fnx in a long while, and I noticed I was shooting about 2-3 inches low at 7-10 yards. Dot on top of the X ring on a silhouette would get shots in the lower 1/3 of the whole target.

I also added a tlr-3 to the end.

Is it just me, or is it the weight of the light, or something else?

I found that my shooting was very accurate with stock sights.  I swapped for the the Trijicon hd's and experienced what you are talking about.  I had to get learn to shoot center of front post, and found it to be much easier hitting 8" pies at 10-20 yards.  It took practice but in the end, it gave me much better acquisition, follow up, and ultimately fine tuning was easier.  

Good Luck!