You've gotten tons of great advice from folks more experienced than I
am, but it sounds like you are making the same mistakes I made when I
was starting out a few years back. My starter kit came with a spool of
7x, and I figured that this was what folks mostly used. Of course I've
learned better; I almost never use that fine of a tippet anymore, and
far prefer 5x or occasionally 6x. I don't think I've fished 7x in any
situation for any of my last 40 outings. I know I've gone through 4 or
5 spools of 4x and not one spool of 7x.

But when I did use 7x, I found that my knots were always a weak spot:
I'd touch the grass on a backcast, and the tippet would snap off at the
hook, or I'd be false casting, and the whole front end would break off
at the leader. I didn't fully appreciate how easily a 7x tippet burns
when tying knots: even now I tend to hold my tippet underwater or in my
mouth when I tighten, and I do it very gently. Its healthy to be
paranoid about burning your knots.

I also found that I was wrapping the line around my finger to get a
grip on it when I was tightening it, sometimes even pinching it a
little against my fingernail, and that was weakening it. If your
midtippet breaks are about 6 inches from the knot, I bet that's what's
happening.

Anyway, take Tim Js advice; don't fish 7x until you've figured out
everything else, as you probably aren't advanced enough to be using it.
That level of stealth in the tippet is probably being undone by a
thousand other things.

HTH, and good luck.
--riverman