When 亏 is kuī ? when yú? The dictionary entry for 亏 is:
亏 kuī(or yú) lose, fail, damage, deficient
When will 亏 be pronounced as yú?
All of your definitions (e.g., 吃虧, 虧損, 虧蝕) appertain to the pronunciation kuī – for this reason, memorising kuī suffices. The pronunciation yú is far less important.

As for the pronunciation yú, it is likely to be a glyphic variant of 于 (a character you have asked before) (see below, from Baidu). From the viewpoint of glyph evolution, the character pronounced kuī was first written as 虧 in traditional script no later than Han dynasty, only simplified into 亏 in the 20th century. The rationale of simplification being, 亏 is a relatively obscure yet graphically related character. Now it has become the dominant meaning associated to 亏.



References:

Baidu Baike
Multi-function Chinese Character Database