That would be weird though, Annie and Armin have barely had any interaction with each other. Annie probably only spared Armin because he was Eren's friend (well either that or she spared Armin for the same reason Mikasa couldn't kill Reiner and Bertholdt).
I really think if there's anyone Annie has a weakspot for, it's Eren, the only time I think Annie has been shown to smile was when she offered to teach Eren more about hand to hand combat.
There's also the flashback in the latest chapter where she grappled Eren for quite some time until Mikasa threw Reiner at them, at that point **** got real because Mikasa looked really pissed.
