From the docs about __block
__block variables live in storage that is shared between the lexical scope of the variable and all blocks and block copies declared or created within the variable’s lexical scope. Thus, the storage will survive the destruction of the stack frame if any copies of the blocks declared within the frame survive beyond the end of the frame (for example, by being enqueued somewhere for later execution). Multiple blocks in a given lexical scope can simultaneously use a shared variable.
From the docs about __weak
__weak specifies a reference that does not keep the referenced object alive. A weak reference is set to nil when there are no strong references to the object.
So they are technically different things. __block is to stop your variable being copied from your external scope into your block scope. __weak is a self delimiting weak pointer.
Note I said technically, because for your case they will do (almost) the same thing. The only difference is if you are using ARC or not. If your project uses ARC and is only for iOS4.3 and above, use __weak. It ensures the reference is set to nil if the global scope reference is releases somehow. If your project doesn’t use ARC or is for older OS versions, use __block.
There is a subtle difference here, make sure you understand it.
EDIT: Another piece to the puzzle is __unsafe_unretained. This modifier is almost the same as __weak but for pre 4.3 runtime environments. HOWEVER, it is not set to nil and can leave you with hanging pointers.