Varys made no effort to stop Tyrion. He wanted Tyrion to kill Tywin. I think Varys was planning on killing Tywin off soon anyway, and having Tyrion do it was just gravy for him.
A dead horse at this point cuz we both agree, but I did re-read the escape chapter in 'Swords, and am officially changing my position
...Varys not only didn't stop him, but told him when they reached the point in the dark passages right below the Tower of the Hand, volunteered that Tywin was in Tyrion's old bedroom, gave him precise directions (exact number of rungs to climb, paces to the hidden door thru the hearth, no less , knowing Tyrion would find Shea there), and then Varys gives this Brere Rabbit routine (just PLEAsE don't throw me in that briar patch!) about folly and throwing both of their lives away once Tyrion starts to climb.
Then the nail in the coffin - the three weapons hanging on the wall in the bedchamber: a pole axe (too long/too awkward for a dwarf) a mace (too high to reach) and the crossbow, underneath which:
"...a wood and iron chest had been pushed against the wall."
It was planned after all, and by Varys. I'm convinced now.