A cardinal rule of baseball: You never want to make the 1st or 3rd out at third base. How does this effect making the 2nd out at third base?
This means you're extremely valuable as a runner when you get to second base. You're in scoring position and just a base hit away from scoring a run. So, why risk stealing third base when it's such a short throw for the catcher to make? You or the coach may risk it when it increases your chance of scoring and you're confident in your ability to make it. Even though it's a shorter throw for the catcher, there are a couple of things that can give you the advantage.
You usually steal third in this situation because of what the pitcher is doing, not because the catcher has a weak arm. Even a catcher with a weak arm can throw out a base runner if they get a poor jump from second. Pitchers, especially young pitchers, often get into a rhythm on the mound. They get the ball, get into stretch, set, 'one-thousand-one' and pitch. When stealing third, lead off in the same way you would when not stealing. You don't want the pitcher or infielders to notice anything different. However, your jump is different. In the timing described above, once the pitcher sets, it's 'one-thous' and you're off. That half second gives you a couple of steps toward third and a great chance of making it. Make sure you don't break too early as the infield will notice and call for the pitcher to step off.
Another key about the pitcher to observer when stealing is the count and the pitcher's tendency with that count. For example, if the hitter has 2 strikes and no balls and the pitcher likes to try and strike batters out with a low and outside curveball, you have, if he throws that pitch, a great pitch to steal on.
Finally, when stealing third, it's a big advantage to have a right-handed hitter at the plate. When the catcher receives the ball and has to throw, that throw becomes much more difficult when he has to throw around a batter.