How do pilots decide whether to circumnavigate bad weather?
Easy.  You don't go through, or close to, a thunderstorm cell (a red area, which is lots of water), period.  You decide on a heading change to navigate around it, request it from ATC, and if the heading you want is not forthcoming, you tell ATC you are altering heading for weather.  You are not required to endanger the aircraft to comply with an ATC clearance of any kind.  And getting close to a cell is endangering the aircraft.

Different airlines will have different policies on some of the details of getting around cells, like they have to maintain 20 miles minimum, upwind if possible.  In visual conditions where you can see the cell, same deal.  Alter heading to upwind side x miles (you don't want to fly under the anvil which is downwind, even if the air is clear in front of you, because you can run into hail falling from the anvil).

Besides thunderstorms, the other big bugaboo risk wise is icing the plane can't handle.  Same deal, you ask for higher or lower, and if icing is becoming dangerous and you need to move now, you tell them you are going higher or lower.