Do we know WHY Varys helped Tyrion escaped? His stance has always been for the good of the realm and that was his reasoning for not helping Ned back in S1. He's always been very firm about not picking sides and then helps Tyrion escape.
I got the impression that he made a one time exception to stick his neck out for someone. With Ned he really couldn't have helped him without implicating himself. And of course Ned's death led to an all out civil war, which played into Varys's plans. He liked and admired Ned, but he couldn't be saved. It's possible he did feel guilty about the situation though, which might have influenced his actions with Tyrion.
Tyrion feels like the only one Varys could truly call a friend. He's one of the few people who had aptitude for playing the game, but wasn't so completely obsessed with empowering himself that he would screw over the entire realm for a chance to wear the crown. This made him a valuable ally (although to Varys ally and pawn are probably closely related). The two conspired together on multiple occasions, and Varys even confided in Tyrion about his life's story. Whether it was personal feelings or he still had plans for him, Varys did not want Tyrion to die.
Luckily for him, unlike the Ned Stark situation, he would not have to raise suspicion on himself for helping. Jaimie would be the obvious culprit for helping Tyrion escape, and it would be difficult to prove who helped him. As long as he could be counted on not to sell Varys out, Varys would be relatively safe (though he would probably be suspected at least).
But when Tyrion shows up and Varys asks "What have you done?", and later when the alarm bells ring and he Nopes out of King's Landing, I got the impression that he was thinking "You've screwed me! The one time I risk myself to help someone else and it bites me on the ass!" With Tywin being discovered dead, the city would surely have gone into lockdown, and Varys would have had no way to justify what he was doing by the docks on the night Tyrion escaped, murdered Tywin, and fled the city. And while he might be able to lie his way out of it, Cercei is the type to pass judgement on feelings rather than evidence, so that would be way too much of a gamble.
He did seem at least sympathetic to Tyrion's situation, and will probably work with him when they get to Essos, but this clearly did not play into his plans. I really wonder how he can get back into the game now that he is a fugitive. The only thing I can think of is joining up with Dany, but Tyrion at least I don't see having much of a role in Dany's group (though he is equally out of options). I do hope the two end up doing something interesting next season.
Based on what do you say that Jaime is a bonehead? There is no evidence that he is stupid. Quite the contrary! He doesn´t care about power, and he can´t be bothered with it, true. But he is not at all stupid! He can be quite cunning and smart and a quick thinker when he wants!
Jamie is by no means dumb. Though he is far too easily manipulated by his sister's ladyparts. But this season at least he proved that he was not completely whipped, and that he could act against her wishes (saving Tyrion) if it was important to him.
