Never allow Player Versus Player rolls

The other answers are tending to how to manage conflict at the table. My solution is that this is one source of conflict that isn't needed at the table. My opinion is that Player versus Player (PVP) rolls easily lead to the dissolution of a group. I don't allow them at my table, and I won't roll them as a player. This is always covered in my table rules document and session zero.

My solution when one player does something like this: P1: "I pick up the gnome! lulz!" DM: "P2, are you okay with this?" P2: "No." DM: "The gnome slips from your grasp." P1: "I roll to grapple!" DM: "Your grapple attempt fails." P1 (not getting the concept yet): "I roll again!" DM: "You take 4 points damage, slip and fall on your butt. The gnome is unharmed and ungrappled." Continue until P1 is unconscious or figures out this isn't okay.

Obviously some fun competition between players when they all ask for it can be an exception here when they're rolling for fun, but allowing one player's character to do anything to another is a recipe for disaster.

Build in ways for players and the DM to communicate discomfort

Some situations, even imaginary, can make some people extremely uncomfortable. It is important to not pressure someone into playing a game that causes them distress. The player who left your table was not necessarily bailing too quickly. They might have been doing what was necessary for them to be okay. Being picked up in the game is a simulation of casual physical violence and a violation of consent. This can be a very sensitive subject.

As Anagkai notes the risk of players being put in distressing situations can be mitigated with a session zero where players and the DM can communicate situations that they won't be okay with.

What you can also do (and set up at a session zero) is create a means for anyone to communicate if there is a distressing situation.
This site offers one such system but you can choose to adapt it to meet the needs of your group. The crucial bit it to make sure everyone at the table knows that they can communicate when a situation is unacceptable for them and that their needs will be respected.

"Is that in character or out of character?"

Whilst it's good to try to catch these issues before they come up in a session 0, some things are not apparent until the game is running. It is impossible to prepare for and anticipate everything, and this situation to me seems like exactly the sort of thing that a session 0 could miss, and needs to be handled on-the-fly when it comes up in play.

Whenever I'm not sure of conflict between players is between the players, or between their characters (and the players are fine with it), I'll ask them. In your case, I would recommend:

P1: I don't want to be picked up!

DM: Is that in character or out of character?

P1: What?

DM: I mean, is that you saying you're not happy with this, or is it just what your character thinks?

This can go one of two ways. Either the player says: "Oh, this is just my character, I'm cool with it, but X wouldn't be!" in which case no problem, carry on, roll strength checks, etc.

Or the player says: "I don't want my character to just be picked up all the time just because I'm small". Now you know this is the player objecting. You might not need to say anything else. The other player (your wife in this case) would likely react with apologies, the "bad thing" never happens (i.e. is retconned), and now everyone is a little clearer on what is and is not ok.

It might be worth having a conversation afterwards to make sure everything is fine, it depends on whether you feel it is necessary depending on how well things seemed to recover in the session.

But what do I do now?

In your situation, the thing to do next, whether you want to invite this player back into the game or not, is to talk to this offended player. Admit that you didn't realise they were offended, not just roleplaying their character being offended.

If you want to invite this player back into the game, offer to discuss ways with the group (including P1) to signal when things bother you out of character, since it's all too easy to assume everything is in character. At my physical table, we use the "time out" hand gesture, but this doesn't work online when you only have your voice, so it might be as simple as just stating "out of character"; or stating "in character" before every in character dialogue. If these terms are agreeable, maybe P1 can rejoin the game and things can continue. If not, then maybe it wasn't such a good fit after all...

You did not have enough information.

What you describe sounds like a rather harmless interaction, a priori. It does not seem like you could have foreseen the results. Therefore, the main thing you could have done better would have been to put yourself into a position to have the necessary information to foresee such problems.

Establish the expectations of the participants beforehand

There is no one correct way to play RPGs, although there can be one correct way for a specific person. If you have a group of players with too different expectations, this will most often result in conflicts and reduced enjoyment for all participants.

Ways to address expectations before the game are a session zero (session to discuss expectations and playstyle with everyone) or the same-page-tool: https://bankuei.wordpress.com/2010/03/27/the-same-page-tool/ (collection of questions to define a specific playstyle). Generally, this allows too divergent expectations to be evident. Then, the participants can discuss what is okay and what not, or leave the game before the first session if no compromise is possible.

Now, obviously, the exact situation you describe will not be considered beforehand. However, if a player designates their character off-limits for such interactions (which I have often heard off with halflings and gnomes), the other players can respect that. If they don't, the divergence in expectations is probably too big. Additionally, even if nobody had thought about such interactions (which are,in the end, harmless), other potential problems could have been identified and it is entirely possible that the player would not have wanted to play in your game in the first place, since it doesn't meet their expectation. Obviously this depends en the other player's experience. If they have never or not often played before, it is difficult for them to assess their expectations.

One example, where I could resolve different expectations beforehand is the following: A friend of mine wanted to bring another (way more experienced) person to the game. I agreed and asked that other person hand in their character. They wanted to use a character they had made for another game, which I said was fine. I quickly checked their sheet and found that their stats were a lot better than the other players'. She told me they had rolled the stats. I was concerned that the high stats might discomfort my other players with point-bought stats, so I asked her politely to modify the stats, expressing those concerns. She didn't want to join any more after that.