How to autohint very thin typefaces?

I try to export a very thin font. The overshoot size is actually bigger than the stroke with:

With the automatic hinting is on, the letter “e” has distorted bottom part (screenshot from InDesign):

So far I could only solve this issue adding a manual hint to two bottom nodes of “e”. Unfortunately this problem affects more letters, is there an easy way how to improve the rendering of the font without manual hinting? Or should I rather switch the hinting off completely for the Hair style?

What are your stems? You should have one H and one V stem with 5u each.

How deep are your zones already? Above 20? Then I would really consider adding a Autohint off parameter to the thin instance.

Not sure I understand this. There is only one hint in your e. When PS Autohinting goes through your glyphs, it will ignore the e because it already has a hint. IOW if you manually hint, you have to completely hint the letter, not just the part that does not work.

My stems are properly set H 5 and V 6. The overshoot zone is exactly 20. But it seams I get better results with Autohint off in this instance. Thanks for your answer.