What happens when two Sword of the Meek are in the graveyard while a 1/1 creature enters play? Do they both get attached to the creature?
Yes, you get to attach both Swords of the Meek.
When the state of the game changes (in this case, because a 1/1 comes enters the battlefield), all objects check if their triggers are 'tripped'. In this case, both the Swords notice the 1/1 entering play, and both will give you the choice to attach them.
The rules for this are in section 603. Handling Triggered Abilities. Specifically:
603.1. Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect]. [Instructions (if any).]”
You control 2 sources that have this.
603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. The ability doesn’t do anything at this point.
The 1/1 satisfies both the Sword's trigger condition.
There are no limitations on how many triggers a state-change can activate.
Both will come back and be attached to the 1/1.
When the 1/1 comes into play, you get one triggered ability for each Sword of the Meek. Then both of those abilities get put on the stack and resolve one at a time. The first one resolves, returning the first Sword of the Meek to play and attaching it to the creature. Then the second resolves, returning the second sword and attaching it as well.