The move out bubble is randomly selected, but the odds of the selection are determined by friendship level. Villagers with high friendship have a lower chance of getting the move out bubble (though it's not impossible unless they are your most recent move-in). Since Merry is at best friend level (indicated by her giving you her photo), she will be less likely to leave unless your other villagers are at best friend level (then the odds even out).
If you have villagers at lower friendship, you could work on getting them up to the same level as Merry's to increase the odds Merry would be selected.
It's kind of complicated, but if you have a rough idea of what level of friendship you are at with each villager, you can figure out the percentages of who is most likely to move next:
villager-moveout-calculator
You may already know this, but you can also try to "move the bubble". Don't finish the conversation or don't talk to the villager with the bubble, exit the game, and time travel a day forward and a different villager might get the bubble.