all my sweeping,hand timings what not is all pretty good (i should know I've been practicing them for the last 2 hours) but during most of that time i had one problem.
the g string would ring after i swept past it (up and down) is there some way I'm meant to mute the string or am i using to much distortion or something?
ive also had a similar problem, im trying to use my palm or thumb depending on where my hands at to quick mute the ringing string. If you play slowly there shouldnt be a ring, i think we just need more practice to get it to the point where its so fluid and percise it wont ring, but for now the thumb and or palm seems to work enough for now lol
It will probably work itself out with more practice, you probably just need to come off the g more cleanly. It's hard to advise without seeing you play.
Yea just try to correct it little by little and it will all turn out good. Basically, that's just practicing!
Here is how I would typically recommend practicing sweeping:

1) Start SLOWLY. Do not, at any point at any time ever during your pick sweeping career think that you can sweep better quickly than slowly. If you cannot sweep slowly, it will not sound good quickly, because you are doing something incorrectly.
2) Your left hand (assuming you are playing on a right handed guitar) should be moving as little as possible while hitting all of the notes. The less that hands moves, the better. You have a lot more to screw up and a lot less coordination when that hand is flopping all over the place. Likewise, when you are practicing slowly you should be concentrating on keeping this hand with tiny movements.
3) Keep your picking hand fluent but firm. There should be almost a "mid point" in the way you are picking, that your hand is relaxed but at the same point you have complete control over your pick. Practice this by just gliding over your strings if you want to.
4) Increase the speed only when your sweep was done perfectly clean. Messy sweeps are shitty sweeps, and shitty sweeps do not sound good.

Good luck!