Why is manoeuvring speed higher in utility category?
There are three factors: Va speed, weight, and CG limit.  

Va is connected to the weight limit, not to the CG limit.  If you look at a typical V/G diagram, you'll notice that Va is defined by the load factor at max gross. Multiplying the load factor times the weight gives the force exerted on the structure at Va.

In the case of the 172, in the normal category at max gross is 3.8G * 2400# = 9120 pounds.

In the utility category 4.4G * 2100# = 9240 (about the same as 9120).

So if the weight is limited to 2100#, the G load can be increased to 4.4, and not exceed the overall structural limits of the aircraft.

The CG limit in the utility category is there to ensure that the CG is forward enough that the pilot can more easily recover from the maneuvers, such as stalls and spins. It probably has a lot to do with the amount of elevator authority, which is necessary to break the stall.