If applying a negative offset, you can't offset more than the available space.
In other words, if the shape is 8pts wide... the maximum interior space is half the width, to allow the path to show you need to keep the offset below half the object width. So, 4pt maximum. Less than 4pts to allow any stroke to show.

Any easy way the "thin" shapes is to apply a black fill, and then a white stroke. AI strokes are centered on the path by default. So make the stroke twice the amount to remove, i.e. if you want to remove 1pt, make the stroke 2pts, want to remove 2pts, make the stroke 4pts thick, etc.
- Make the stroke as wide as you want until the black area is as thick
as you want.
- Then select the objects and choose
Object > Expand
.
- Then click the Merge button on the
Pathfinder Panel
- Use the Direct Selection Tool (white arrow) to click one of the
white shapes.
- Choose
Select> Same > Fill & Stroke
from the menu.
- Hit the Delete key to remove the white shapes.
You are then left with only the (thinner) black shapes.
