It's impossible to answer the question "should I train or level during 2x exp?", it highly depends on your goals.
- If your goal is to get the highest lvl possible, then obviously, it's better to hunt.
- If your goal is to get skills, then obviously is better to train.
Both will advance 2x as fast, so it just depends on what you want for your character....
Personally, I level when I have a team or a good solo respawn, and I train when I don't have either, so I don't "waste" time. But my priority is always to level, but some people will just prioritize skills... thats why theres no way to give a proper answer here...
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Now, about the question: "is it worth using training weapons on 2x exp?", IMO yes, totally. If you have money to spare, it's a good way to make your character much stronger, specially if you are a mage and even more if you have a private dummy to use!
Here's why a private dummy is so good: https://www.tibiaqa.com/13793/whats-difference-between-exercise-dummy-store-compared-public-exercise?show=13793#q13793
Here's some nice calculation on what it means to use a Exercise Rod/Wand (check best answer): https://www.tibiaqa.com/966/whats-the-best-way-to-train-magic-level-on-double-exp-weekend?show=966#q966