Those two-top tables can be tiny--just barely large enough for two trays. So even when I'm eating alone, I might go for a four-top, so I'll have room for my book or laptop.
If you asked to sit with me, I'd be surprised, if there were empty tables available, whatever their size. Around here, you only ask to share a table if you can't find any other place to sit.
It makes a difference to me how many people would be sitting at the shared table. Two people, four places--there's still a bit of empty space at the table and the couple could talk to each other and I could tune them out. I'd still have half the table to spread my things out. There's a small buffer zone.
Three people and I'm surrounded. There's no way to avoid their conversation, the fact that someone is either sitting on both sides of me or across the table (depending on the shape of the table). I'm now in the middle of whatever is going on with the other people at the table. And I'd be imagining that they are all sitting there wondering why I'm still there--clearly I should be able to see that they want the whole table.
I wouldn't move, but I'd finish my meal as quickly as possible and leave, thinking very poorly of the people who wanted to sit at my table when there were empty tables available.
In fact, I couldn't honestly give you an answer right now as to whether or not I'd let a group of three sit at a four-top table with me. Because the more I think about it, the more I'm inclined to refuse, unless there isn't any other table available.