Nobody needs to request a weather induced deviation from the cleared track/airway, but you need to request an appropriate route to avoid conflicting traffic, and you will be cleared to follow a heading or off-track distance. Give that controllers a chance to keep you out of other aircraft's way!
"XXX, request H250 to avoid wx." - "XXX, cto avoid conflicting heading, can you accept H260?" - "XXX, negative, we need to turn further south to avoid." - "XXX, (fly H235, H235 approved to avoid), advise when able to turn on course!" (same for x NM r/l of track)
Actually, it's easy! Do what you need to do, and try to communicate it in the best way possible.