I'd like to build a person from triangle-like shapes - white shapes with black strokes, but my problem is that even though I start to build each shape using at least one side of the previous triangle (like in the screenshot), the strokes overlap, but I cannot adjust them to looko as if there was only one stroke, they are always too thick.
Another way is to draw the main outlines as polylines and divide the interior. There's no need to draw the same line twice. See the cartoon (I had a locked grey rectangle in the back to make white visible)
The outline drawed with the pen (it makes easily straight gapless polyline by clicking only)
Line segments were drawn with the line tool. Be sure you have the Smart Quides and Snap to points =ON. Otherwise you easily have some gaps.
You can well use in 1...2 a black stroke and finally fill the outline area with white and send it to the background => Ready.
If you want to make separate colorings to the areas, you can create those areas with the live paint bucket.
The Live Paint Bucket is used to fill the areas between the strokes. The red highlight shows the area to be filled.
The result was expanded (=expand only the object, not fills nor strokes), ungrouped (needed several ungroup commands), one white triangle was selected and in the select menu all with the same fill was taken along. All selected got a black stroke and were dragged aside.
The white areas are now separate shapes. It's easy to give some different fills or strokes, if needed.
This reminds me of an issue some people that are new to AI encounter. I guess your have an inconsistency in stroke positioning. I would suggest selecting all your strokes, go to the stroke panel and align all your strokes to center, rather than inside or outside