Seeing that lashon hakodesh allows for analyzing the connection between similar rooted words, what is the connection between liver (כבד) and honor (כבוד)?
Shemot 7:14 says:
וַיֹּ֤אמֶר ה' אֶל־משֶׁ֔ה כָּבֵ֖ד לֵ֣ב פַּרְעֹ֑ה מֵאֵ֖ן לְשַׁלַּ֥ח הָעָֽם
The Lord said to Moses, "Pharaoh's heart is heavy; he has refused to let the people out.
The word “kaveid” means “heavy” although I believe some translate this here as "stubborn" in the Torah. Why not say his heart was “kashah”: “hardened” or “ikeish”: "stubborn"? One explanation is that “kaveid” also means “liver” and liver must be broiled and the more it is broiled, the harder it becomes. Usually, when a stubborn person is beaten and punished, his heart softens and he begins to concede and yield. So the Torah is telling us that the heart of Pharaoh was like liver: the more plagues he received, the more stubborn he became. (מיוסד על מדרש רבה שמות, ט,ח)
That was an interesting fact from the Torah and Sages to tie it altogether with the other translation "heavy" as some in the comments noted.
To answer your question:
So how does "liver" relate to "honor"? Your liver is the hardest working organ in your body, performing over 500 life-sustaining functions. It is the largest internal organ in the body and filters toxins from your blood, produces digestive enzymes called bile, stores vitamins and minerals, regulates hormones and the immune response and helps clot blood. Your liver is the only organ in your body that can regrow after parts of it have been removed or damaged. In fact, your liver can grow back to its full size in just a matter of months.
Can you live without the liver though? NO. The liver is so crucial to existence that while you can live with only part of a liver, you can’t live without any liver at all.
In fact, we can live without various body organs... but not without the liver. Just as we cannot survive without our livers, we cannot have success in our lives or survive without any honor. But perhaps a lesson to take from the connection between "honor" and your "liver" is that just like how if you lose a part of your liver it can regrow... so to if you lose a part of your honor it can be regained.