You get better SP by equipping a better weapon.
When you receive SP for hitting a mob, the amount you receive is influenced by the difficulty of the mob, and how much damage you do. There are other factors that come into play, but we don't really know what they are yet.
I've tested this as a DoW and a DoM. In both cases my SP gain was better when using a better weapon.
The thinking some players have is that using a weak weapon is better because it gives you more chances to earn SP during a fight, since you will be attacking more times. And that is true, it does give you more chances. But that thinking doesn't take into account the smaller amount of SP you will earn.
Suppose a mob takes 20 hits to kill with a weak weapon, and only 12 to kill with a stronger weapon.
Now suppose you get a skill up on 10% of your hits.
Using a weaker weapon, you will earn SP twice during the fight.
Using a stronger weapon, you will earn SP once most fights, with an additional skill-up every 5th fight (1.2 skillup rate).
Now suppose the weaker weapon will gain skill at 30SP, while the stronger weapon earns skill at 50SP.
In the fight with the weaker weapon, you will have earned 60SP. With the stronger weapon, you earn 50SP.
Over the course of 10 fights that comes to...
Weaker: 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 + 60 = 600SP.
Stronger: 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 = 500SP.
But don't forget to factor in the 0.2 skillup rate for the stronger weapon, which adds another 100SP.
Meaning at first glance they appear to come out even. But now consider how many hits it took for each.
Weaker weapon: 200 hits total.
Stronger weapon: 120 hits total.
In 60% of the hits you earned the same amount of SP. Less hits means faster fights, which means less downtime. Less downtime means you can fight more mobs, which then pushes the better weapon's SP gains beyond the weaker.
However, all of this is working with constant figures. Which as anyone who has done any grinding can tell you, SP gains are not constant. I've gained over 250SP from one mob, then right afterwards killed the exact same mob type/difficulty and earned 0SP. But in the cases when you do earn SP, maximizing the gain by having a better weapon is your best option.
Another thing to remember is that a better weapon also means better accuracy. Which means more hits landing in a shorter period of time. That increases the SP rate over the weaker weapon even further since you're not wasting so much time missing. Missing will never give you SP, so it is something to be avoided if SP is your goal.
Lastly, don't fight mobs that you can kill in 2 hits. Fight mobs that can take a few of your attack skills. In the times where you earn SP from using a skill, the gain will be greater than what you'd receive from several of your basic attacks. It doesn't work so well with spells though. If you're a conjurer, I'd suggest spamming basic attacks and using Radiance whenever you have the TP. Regardless of your class, always try to end the fight with a skill. You may get lucky and get that big boost of SP.