Bad weather can cause some bumpy condition on a flight, but remember for the most of it you do actual fly 'ABOVE' the weather.
I understand why you ask as I am a nervous flyer myself. I can tell you what I do to 'mentally' prepare for a flight. They may work for you, they may not. You need to find you own method that works best for you.
I never check the weather until the day. US weather changes so fast there is no point in looking at weather to see what the potential for a bumpy flight is.
On the day I check the following sites:
http://www.turbulenceforecast.com/ This is a good one as it is up to date and shows 'no turbulenece' reports as well as 'turbelence' - it also gives height that turbelence was experienced
http://www.weather.com/maps/activity/av ... large.htmlThis can look a little daunting, so I prefer the first one, plus it only shows you turbulence over mainlaind US and if you are flying to New York you don't really do much over mainland.
Also, once on this page check where the jetstream is and then as you track your flight across using the skymap you can expect a little bumping as you move in and out of the jetstream.
http://uk.weather.com/maps/lifestyles/i ... large.htmlCheck this to see the wind across the atlantic. In my experience you get bumps sometimes where the arrows cross the path (rather than going with it or against it). Low winds speeds don't normally cause to much problem.
By using these I can see where I can expect bumps. For me, just knowing potential when the bumps will end is comfort.
Lastly, remember that most people hurt in turbelunce are not strapped in. Planes are designed to take an amazing amount of bumping during a flight. Far more than you would imagine - So don't worry and picture yourself on a theme park ride somewhere.
Hope this help and good luck
Paul