I know in general terms how to use "very much" but since my students started making specific questions and writing sentences like the one above I got very confused (I'm brazilian, and I just started working as an English Teacher).
I would say that the sentence would sound better if it was "I like to play volleyball on weekends very much", but I want to understand what positions it could be placed and how it would change the sentence's meaning.
Best Answer
As John says, "very much" modifies a verb phrase. It means the same as the more casual "a lot" or "a whole lot". It's most natural position is after the verb phrase that it modifies, just like "a lot", but unlike "a lot", it can also go before the verb phrase that it modifies or after the main verb of that phrase.
When "very much" modifies a preceding complement construction, there is often a distressing ambiguity about whether it modifies the main verb phrase or the complement verb phrase: "I prefer not to eat snails very much" could mean either that your preference for not eating snails is extreme, or that snails are okay if indulged in only occasionally. That ambiguity is resolved by moving "very much" to a position either immediately before or immediately after "prefer", because then "very much" can only modify the entire verb phrase with "prefer".
On the other hand, "a lot" cannot be disambiguated in this way, since it has to go after the verb phrase it modifies. I think that this sort of disambiguation is mainly what "very much" is useful for, at least in casual conversation.
When "very much" comes before the verb phrase it modifies, it follows auxiliary verbs or other adverbs: