I used to worry a lot about finances. I drove my DH crazy with it until finally he asked me, "do we pay our tithing? have we ever gone in need? hasn't the Lord always taken care of us?" and a bunch of other questions that really made me think. I was and am doing the right thing in that area and don't need to WORRY about it. We will be blessed (and have been) to be able to take care of what needs to be taken care of. I need to do my part in being careful and keeping track and then stop thinking about. Now when little concerns about it creep in, I run myself through those questions and then I'm able to drop the worry. It is still hard when the budget is stretched tight, but for the most part, I can not worry about that one.
To continue worrying is like 1 Nephi 3...the end of the chapter where Laman and Lemuel say "he can slay fifty, then why not us?" after they've seen an angel telling them the right thing to do. I think that worrying beyond a certain point becomes somewhat insulting to our Heavenly Father...as if He will not do his part when we've done ours. He's promised He will and when He promises...He will.
So if I find myself in too much worry, I just need to think through my part...have I done it? Did I do all that I could? Then the rest isn't in my hands and that's ok. It's wonderful to see the works of Heavenly Father come forth after we've done our part of them.
Hope that helps! It always has for me.