Well apart from the Cyclone mechanics (that little tornado counter thing on the bottom of the screen above the meter - that shit is actually kinda complicated and its really not something to be focused on initially with akihiko imo), they offer invincibility from high/mid attacks and build meter. This means that you can get around almost all projectiles in the game. Liz will give you some issues because her beam is wide as hell and Yukiko's non-fan zoning attacks too.
The thing about the weaves and the dashes is that they offer options that a typical roll doesn't. You can cancel out of them into other moves such as his hook and kill rush - this means that you always have tons of options open in most immediate non-pressure situations such as the option to cross full screen damn near instantly, dash-roll/dash-roll-hop crossups and mixups, weave and counter, dash-throw, etc... it goes on for days. You can also cancel into his counter, sweep, other dashes, etc. So even though Akihiko's isn't a "fast" character, he operates faster than most if that makes any sense.
It just takes a lot of familiarity with your own options and matchup awareness with Akihiko.