This is a bit difficult to answer. I tried to find a rule/material about it but I couldn't. However, I noticed that we use "milyen" mostly with nouns or with the verb "lenni" in various conjugated forms. "Milyen ételeket szeretsz?" (What kinds of food do you like?), "Milyen verset olvasol?" (What /kind of/ poem are you reading?"). However, the meaning would be different with using "hogy". In this case, the verb comes right after the question word. "Hogy szereted az ételeket?" (How do you like the food? /Raw, baked, etc./., "Hogy olvasod a verset?" (How are you reading the poem?) /Silently, loudly, emotionally, etc./ I hope it makes sense. Remember, that in the question "How was your weekend?" you refer to the weekend and not the action/verb. I guess that's why we translate it as "Milyen volt a hétvégéd?", because we refer to "hétvége", which is a noun. Plus, in the present tense, we don't even use a verb in this case (milyen a hétvégéd? vs. hogy telik a hétvégéd?) --> this should support the idea of the different uses of the two question words.

Hogy telik a napod? Here the "hogy" (hogyan) means "how". ~ How do you spend your day? Milyen a napod? What is your day like? Milyen volt a hétvégéd? What was your weekend like? Milyen a leves? What is the soup like? So the "milyen" means "what ... like" Hogy volt a hétvégéd? - The sentence is understandable but we never use it like this. Hogy telt a hétvégéd? is the correct one.