Is there an easy way to do this?

Is it dependent on monster level or player level vs monster level or you just need to use your weapon X number of times per weapon rank?

I've tested this, and it's just how many kills you get with the item equipped. So I equip two items that needs to be leveled onto a character or two and have those two duo clear maps quickly. Monster portal/weak slimes help with easy leveling up.

Of the top of my head I can't think of a map with many fast spawning low level mobs- is there a consensus on what would make the best map for this?

This is probably not the best way to do this, but here's what I did and it was quite fast.

In Baked Clay Foothills, there is a section to the left that requires lavawalk, but there's 2 monster portals right next to each other. These lavaworms are somewhat hard to kill, but Emelita's Water Bullet or Suina will OHKO/2HKO them easily. If you want, leave Serawi 2 spaces away to heal Emelita/Suina.

I think that AURU486 asked about Weapon Skill in character status and that one is somewhat more complicated than level of a weapon. Second one as stated above depends only on number of enemies killed, while first one is a little different and from what I can gather from japanese wiki it depends on how much you hit an enemy, whether you crit and how many same enemies you have killed (if I am not mistaken, the more same enemies you kill, the more weapon skill exp you get).

As for map with many fast spawning low level mobs. Personally I like Amurent Forestland/Junble Tribeland. There are 3 portals close to home base, next to each other. Two of them have 1 monster per 4 turns spawn, and one has 1 monster per 6 turn spawn.
Demonic Banquet is really good if it comes to number of enemies (12 portals near home base), but it's not "low level".

The level is based on kills
Lv 0 - 1 = 5 kills
Lv 1 - 2 = 12 kills
Lv 2 - 3 = 15 kills
Lv 3+ = 25 kills