What rhyme groups had "light" labial initials (輕唇音) such as 非 in the Yunjing (韻鏡)?
The following answer is a translation and summary from Lin (2013:6-8). This also serves to supplement C.K.'s observation.

Rhymes placed in grade III include eight chongniu rhymes (重紐八韻), ten labiodental rhymes (輕唇十韻), and normal grade III rhymes (普通三等韻).

Openness is determined by the absence of the rounded prenuclear glide /u/ or /w/. The following is a table that summarises the openness (column 2) of each labiodental rhyme (column 1) reconstructed in five references (from left to right: Kalgren, Li Rong, Dong Tonghe, Baxter, Zhu Jianing). The fact that three out of ten labiodental rhymes were unanimously reconstructed as kaikou (東三, 陽, and 尤), and that two were either reconstructed as kaikou or hekou (鐘 and 虞), violates the traditional rule that 'grade III hekou is the phonological environment for the labiodentalisation of /p/ to [f]':

In Lin's words,

若是傳統說法中的合口三等是指開合口之分，勢必與韻鏡的分類不符。
If the traditional saying hekou sandeng indeed refers to openness (i.e. absence or presence of the rounded prenuclear glide /u/ or /w/), then it is bound to differ from Yunjing's classification scheme.

Note

/j/ is the necessary prenuclear glide to have the rhymes classified as grade III.
The 東三-rhyme is not hekou because /u/ is not prenuclear.


Lin further noticed alternative phonological rules were proposed for labiodentalisation in MC:

(Grade III hekou rule) /p/ → [f] / _ [j] [w] V
(Baxter 1992:47) /p/ → [f] / _ [j] [V, +back]
(Yang 2005:147) /p/ → [f] / _ [j] [V, +central, +back]

which certainly are more lenient. Baxter permits not only [w] but all back vowels (ranging from [u] to [ɑ]), whereas Yang even permits central vowels. Yang's rule is more flexible (Baxter did not use much central vowels except /ɨ/), but not without fault. Lin argued with Yang's rule, words of the 蒸-rhyme would also undergo labiodentalisation (presence of mid-central vowel /ə/, see below, from Wiktionary), although 蒸-rhyme is not any one of the eight known rhymes:





Zhengzhang Shangfang
Pan Wuyun
Shao Rongfen
Edwin Pulleyblank
Li Rong
Wang Li
Bernard Karlgren




蒸
/t͡ɕɨŋ/
/t͡ɕɨŋ/
/t͡ɕieŋ/
/ciŋ/
/t͡ɕiəŋ/
/t͡ɕĭəŋ/
/t͡ɕi̯əŋ/




Lin subsequently proposed the following phonological rule

/p/ → [f] / _ [j] [+rounded],

where [+rounded] means EITHER a rounded prenuclear glide (/u/ or /w/, or the hekou element) OR a rounded nucleus. Obviously the first part corresponds to the hekou sandeng rule. The second part accounts for any remaining inconsistencies. Sadly, there is one exception: the 陽-rhyme (neither /a/ or /ɑ/ are rounded). So to compensate for that,
 
                    [V, –front]
 /p/ → [f] / _ [j] {           }
                    [+rounded]
 
was proposed. I think this is a big improvement from the historical hekou sandeng rule.


References

林智凱（2013）〈中古漢語重紐、輕唇與普通三等三者交互關係〉。

Baxter W. A Handbook of Old Chinese Phonology. Berlin: Mouton De Gruyter; 1992.

楊劍橋（2005）《漢語音韻學講義》，復旦大學出版社。


Appendix: IPA vowels and their backness