As you can see, the Sophons are friendly towards me, we have a common enemy and evidently would be happy to have a science treaty. If I ask to balance, they will even give me quite a lot of good stuff. But they steadfastly refuse to sign the science treaty! Why? Is it that they can't afford the influence cost to keep it going? Is there any way around that?

They probably do not have enough inflence generated to cover the cost of the treaty

And I can't just give them influence... Got to say this seems like one of several places where the game's systems just don't work. Not least because the in-game messaging gives you no indication that this is what is behind the problem.