On the one hand, it seems safe to say that not all aesthetic appreciation is enjoyment. There are some works of art that are profoundly disturbing, and yet we still value them. An example: I remember vividly the first time I saw one of Ad Reinhardt's large black canvases. I was taken by surprise: I didn't expect to have much of a reaction, and yet I felt something for which the word "despair" is about the best label I can come up with. I found the experience moving, but it feels wrong to call it enjoyable.
Still, there are other works of art that we do enjoy and that are beautiful. So let's turn to those.
Take an example of some work that you find beautiful -- perhaps the third movement of Beethoven's opus 132 A Minor quartet. If someone asked "Why do you enjoy listening to that?" saying "Because it's so beautiful" would be a perfectly good answer, though there's a great deal more that one could add. If your friend then asked "But why do you enjoy beautiful things?" you might find the question a bit perverse. One can imagine replying "So I should enjoy nasty things instead?"
The larger point is that beauty is a "response dependent" property. The idea that something could be beautiful apart from all possible responses to it is hard to fathom. More to the point, it's at least plausible that the capacity for eliciting a kind of enjoyment is part of what it is for something to be beautiful. In that case, there's a conceptual connection between beauty and enjoyment. Of course, the person experiencing a beautiful object must have the capacity to respond -- not everyone "gets" Beethoven's music, for instance -- but beauty still isn't something that floats free of all possible responses. (You might also have a look at question 1788.)
There's yet another question we might ask. It may be that all beautiful things have something in common that we can describe, say, in purely formal terms -- no reference to responses, and no mention of beauty as such. We could then ask: why do we find things with those formal properties enjoyable? That's a perfectly good question, but alas, not one that philosophers are in a particularly good position to answer. It's something in the way we're wired, as we might say, but what it is about our wiring and how it came to be that way is a question for the sciences.