Welcome Dude,
Yeah, this can get confusing.
First - It may seem counter intuitive, but with negative film, there is no direct link between the camera exposure and the finished positive. In fact there is a whole range of acceptable exposure settings that will work just fine.
A negative is simply an intermediate storage medium. Choices/Adjustments MUST be made when printing to make acceptable prints. There is no exception to that rule. Setup of the enlarger (or scanner/software) is a variable that must be dealt with by active choice or default or automation.
Now the frames you shot at 800 should look darker/thicker than the frames at 1600. That does not mean the frames at 800 are over exposed, in fact unless you were shooting at 100 or a lower number, I'd suggest that you are nowhere near a true over-exposure (loss of important highlight detail/shouldering). At 800 and even more so at 1600 you are more likely to still be at the underexposing (losing important shadow detail) end of the world.
Thicker negatives simply require more printing exposure than thin negatives. It's just a printing adjustment.
For example when I shoot HP5 I prefer to shoot between 100 and 800 but will shoot at 25 or 1600 if needed, and I don't adjust film development, I'll run all these exposures on the same roll if need be. My norm is to develop as per instructions for 400 regardless.
I can make prints from HP5 shots at 100 and 800 that are essentially identical. HP5 is very forgiving of exposure variations.
Second - Pushing development does not change the sensitivity of a film significantly. Pushing is the equivalent of what Ansel Adams called "plus" development. Pulling is the equivalent of "minus" development. The real purpose of adjusting development is to change the look/snappiness/contrast of the print, not to change sensitivity.
This was important because Ansel and those before didn't have the same tools we have today. Their normal papers were "single grade". Development changes used-to-be used to change the look of the print, because it was hard to adjust the paper.
Today variable grade papers (and digital) have to a great extent eliminated the need for adjusting film development. Today we can more easily fix-it-in-post. We just choose different settings.
The films we have today are also more forgiving than what Ansel had.