I normally keep the top up until I feel like going topless, which happens about every other day. I just get annoyed because why should drop the top, so I can put it up again when I arrive at wherever I am going in a few minutes.
My criteria for dropping the top is the angle of the sun (will it be right in my eyes the whole time), and am I going to be driving on the freeway or by any dusty construction sites.
So to answer you question I don't thinks it weird to leave the top up.
