Just to clear up the terminology:
- Grind Cap: How high you can grind a weapon, which is increased by feeding duplicate weapons.
- Grind Level: The actual grind on your item, ie. +8, +27, etc.
Now, assuming your Grind Cap for your weapon is at 35, you need 480EXP to increase Grind Level by one from +30 to +35, so to increase from +30 to +35, you need a total of 2400EXP, which is roughly the equivalent of using 4 or 5 +20 10* weapons as fodder (basically, there is no reason to get a 13* weapon to +30 if you are going to just use it as fodder, especially if the Grind Cap is already 35).
The main benefit of using Same Name weapons is to increase the Grind Cap, but keep in mind that if your weapon's Grind Level is at its current Grind Cap, using the duplicate weapon will only increase the Grind Cap, but not the Grind Level.
So in your scenario, you have two identical +30 weapons whose Grind Cap and Grind Level are 30; if you feed one to the other, you will merely unlock the Grind Cap to 31, but the weapon will stay at +30 (ie. any EXP that could have been gained is lost).
Now, let's say you have 2 duplicate weapons, one is +20 with a Grind Cap of 32, and the other is +5 also with a Grind Cap of 32; using the latter as fodder for the former will result in the Grind Cap being increased to 35 as well as it getting EXP for its current Grind Level.
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