What benefits are there in giving your followers better [magical] weapons? Should I craft them weapons?

Solution 1:

The higher the dps of the weapon, the more damage the follower will do. Additionally, ability modifiers on the weapons will help them and/or you directly.

Followers contribute 20% of their added Magic Find, Gold Find, and XP bonuses to you. Effects that gain them life on hit or kill will allow them to survive much longer. Ability modifiers such as Dex, Vit, Str, and Int will give them 2.5x the benefit that similar effects will grant you.

While they're never going to do as much damage as you will, they do contribute significantly to solo play, and are capable of killing monsters on their own. Improving their gear directly improves their ability to do so.

In addition, certain gear abilities can also trigger from follower attacks. Most notably, giving your follower a weapon with +cold damage will give a (very) minor snare effect to any enemies they hit. This is particularly effective when used on the scoundrel, in conjunction with his attack that fires three arrows at once.

Solution 2:

Of course, as Beofett said, you gain 20% of MF, GF and XP bonus back from their gear, so that helps. However, there's still the question of how much they help you in actual combat. To answer this clearly, you have to look at it from the perspective of different difficulties:

On normal, they are already not exactly insane DPS-monsters, but they do help quite a bit. Especially low-HP monsters can be quickly dispatched by them, as long as you keep them geared well, but they won't make a noticable difference in boss fights, for example, in terms of damage done.

However, in difficulties higher than normal, I think the Templar will really shine as an excellent tank. He has some good crowd control abilities (he's able to stun and slow down enemies, as well as taunt them to make them attack him. He can also protect you from dying when you get low on health), and his ability to use a shield will most likely work wonders. For this reason, it will be incredibly important to keep him geared up with vitality-gear.