In RM2 (and in RMSS, before Martial Arts Companion was added), Weapon Katas worked as follows:
1) Using a Weapon Kata incurs a -20 modifier to the OB.
2) First weapon kata is gained when OB of 50 is reached (usually knife for Strikes, and stick for Sweeps), and two additional kata when that Rank/Tier has an OB of 90 or higher (yes, 3 weapon kata for EACH tier/rank of Martial Arts).
3) When using the Weapon Kata, attacks are made on the appropriate Martial Arts attack table. However, the weapon kata deals an amount of extra damage equal to the different of the max damage from the kata weapon's table minus the max damage on the MA attack table, for that given AT.
Thus, a Battle Axe would do the following extra damage for the given ATs
AT 1 (+21 hits)
AT 2 (+20 hits)
AT 3 (+21 hits)
etc.
AT 18 (+8 hits)
AT 19 (+8 hits)
AT 20 (+9 hits)
4) In addition to the normal MA critical strike (if any), the attack also deals an appropriate critical for the weapon, of one less severity than the critical delivered on the MA attack table. Only 1 roll is used for BOTH criticals. If the kata attack uses the Sweeps table, then the extra crit is ALWAYS an unbalancing crit, otherwise it is the most common crit for the weapon used.
In RMC, this changed a bit. You can find the RMC/X kata rules in either Express Additions #2, or in Combat Companion.
Essentially, the rules are simple, you have to pay DP to acquire a Kata. The character must have enough ranks in the proper Tier/Rank of Martial Arts to purchase/use the Kata though. Also, each kata can do an alternative crit, which is normally one severity less than the one indicated on the table, and the kata weapon does a specific amount of extra damage (some weapons give other benefits, like multiple choice on which alt crit to use, or an alt crit that is of equal severity, etc..)
For Example: a Quarterstaff requires at least 5 ranks in Tier/Rank III Martial Arts (strikes or sweeps), and it costs 8 DP to acquire, and it must be purchased separately for Strikes and Sweeps). When used, the character will deal 8 bonus hits on each attack that deals damage. The Alt Crit is Krush, and is of equal severity. Also, if the Quarterstaff is used as a weapon kata for Sweeps/Throws, the character gains a +10 to his OB with Sweeps attacks.