I don't understand how it's possible to download something "for free" if there is a charge for it. Usually such things can't even be viewed in their entirety or downloaded unless you pay first, at least what I download which is books and sheet music.
If there IS a charge for it and you don't pay, then I would think it IS a sin because you're not doing what the provider requires. Perhaps that money is to go towards maintaining the web site or in the case of sheet music where you might need enough copies for a group of musicians or singers, the publisher would indeed be losing money if someone downloaded just one copy and then reproduced that copy and handed it out to others whether they themselves charged the others for the copy or not, which would entail committing another sin in itself unless the original publisher stated that you were allowed to make additional copies (the number of which is usually stipulated) "for educational purposes" and such. What they don't want you to do basically is turn around and sell their stuff and profit from it instead of them, which is quite reasonable.
Then there's the matter of copyright infringement, which I won't even begin to get into. It's just best to obey the policies of the web site. I try to find things that are free even if it means searching longer or using different search engines. That way no worries if I want to pass it on to someone.