When was the first time you ran Tales of Symphonia in Dolphin? That is to say, which revision at the time were you using? Your CPU is pretty underpowered for Dolphin; it may be the case that newer revisions are simply more demanding than the revision you previously used. You can go back to whatever revision you were using beforehand, just note that revisions prior to the 4.0 release are not supported any more.
I was using Dolphin 2.0. The first time I ran the game using Dolphin it worked perfectly, shooting into 80-90 FPS while playing, 60 with the framelimit in place. If upgrading is really the problem, then I can just go back to Dolphin 2.0.
Dolphin 2.0 used Direct3D 9, so I tried to use that setting on Dolphin 4.0. Audio also stutters badly, even using OpenAL and Latency cranked up to 6.
EDIT: The first time was about three days ago.
There's your problem, as I suspected. Old builds and revisions used less CPU resources than 4.0 and the latest development builds. To get the same speed in 4.0 as you had in 2.0, you'll need a better CPU, and with laptops, that most often means getting a new machine. The short story is your CPU is too weak for this game in recent revisions.
/godfkingdammit.
Thanks for your help. Sorry for wasting your time.