I always thought vážit si was more like "appreciates" vážit si toho, "I appreciate that".
It has slightly different meaning when used with objects and when used with people I think.
When I look at the English sentence "Matěj respects his father.", then the difference between Czech verbs "vážit si" and "respektovat" comes to my mind. Obviously, "to respect = respektovat", there is no doubt about it, but since the two Czech verbs are not perfect synonyms (You can "respektovat" your boss, but if he is an ❤❤❤❤❤❤❤, you'll definitely not "vážit si" him.), there must be some way to express that in English too. And I feel that James might be correct in this one. The verb "vážit si" definitely shows some appreciation. The respect is only a natural conclusion when you appreciate someone/something. Thoughts? :-)
Proč se u této věty nepoužije OF - "Matěj respects of his father", když například u další věty "Já se jí nebojím" je to OF použito - I am not afraid of her"?
"Respect" is a verb and can be used with an object (his father). No need for preposition OF ("Matěj respects his father"). But "afraid" is an adjective and "of her" is modifying that adjective, so it needs the preposition. Similar to "I am happy FOR her". If we use a verb instead of "afraid", we don't need OF. Eg. "I do not FEAR her".