If I understand your question correctly you are talking about super thin fonts and their contrast requirements.
There are no requirements if a font is super thin in terms of WCAG, 508 etc. that are any different than normal weight fonts.
That being said, it isn't about requirements (and too much focus is put on requirements and not enough on the end user).
If you are using an especially thin font I would recommend adding 50% to your colour contrast requirements.
So for standard text at 16px up your requirements to 6.75:1.
The reason for this is anti-aliasing causes colours to 'bleed' into each other to round corners and edges, by upping the contrast these pixels have a higher contrast (think of it as 3 pixels next to each other -> grey, light-grey, white. If you have higher contrast set then these pixels become dark-grey, grey, white so the contrast between each 'step' is higher and therefore the letters are more pronounced.)
Ultimately you should ask the question 'can we use a thicker font here' and adjust your design to use normal weight fonts as that would be preferable.