The advantages of the heavier barrel are:
1) Stiffer - greater accuracy potential
2) More shots before overheating - longer barrel life and greater accuracy at the end of long shot strings
3) Heavier gun - easier to shoot accurately

So the heavier barrel is favored for:
1) Situations where you'll shoot fast enough to overheat a barrel - preserve accuracy and barrel life
2) Care about maximal accuracy - longer range shooting

Your situation sounds like it does not demand a heavier barrel, though you could still opt for it. The only real trade-off is weight, and you'll have to make that decision.