I don't personally re-buy free stuff or pay again for things I already own in another format (with a couple of very specific exceptions). And I've never been inclined to the tipjar method, but if it works for other people, that's great.
What I do instead is pay for something else that's non-free from the author/publisher, even if it isn't nearly appealing as the free thing (provided it's at a reasonable price) and thereby hopefully they're supported for their generous free offering and I also get to try something else by them at the same time.
I've gone and bought a series by one author which only looks middling-promising on the strength of his having put up some books-in-progress in serial format from his other series which I actually like as free reads online.
Mind you, I did it during those Fictionwise 50-60% off coupon sales because I'm cheap and there are limits.
But I'm pretty happy to support people orthogonally in return for their free giveaways, even if I'm a bit reluctant to spend my money recompensating them for those particular titles directly.
I think this sort of thing was noted in one of Eric Flint's editorials up on Baen, about how after they put a bunch of Mercedes Lackey's stuff up free in the Library, she got a sales spike for the print books in her series at another publisher.