The first portion of this saying is easy to translate from the original Hebrew, and easy to understand. Honey is delicious and nutritious, but too much of it brings problems (see Proverbs 25:16). The second part of this saying is rather unclear. Literally it says, Examine their honour.
What is meant by this?
There is also the question of how both portions of this saying relate to each other. Is this meant as a comparison, or perhaps as a contrast?
The translators have hesitated about this, and when you compare several translations, you will see large differences. That already becomes clear when the New Bible Translation says, seeking excessive honour
and you compare that with the English Standard Version translation of nor is it glorious to seek one’s own glory.
It is for that reason that at the bottom of the ESV page, there is a notation: The meaning of the Hebrew line is uncertain.
It seems most likely to me to apply the not good
here to the first, as well as the second portion of this saying. To eat an excessive amount of honey is not healthy, and similarly, it is not healthy to credit yourself with excessive honour. This may refer to your own honour but also to honouring someone else.
This attempt at explaining the text seems better to me than fabricating something from the Hebrew text (the various manuscripts provide no grounds for this), which happens in several translations.
27 It is not good to eat much honey, nor is it glorious to seek one’s own glory.