I did a test by draining the battery to 26%. Then when I start charging, the charging current is shown as ~850 mA. This is with Wifi on, and screen brightness set to Auto.Then when I increase the screen brightness to max, guess what, the charging current is either 0 or shown as discharging, which means the battery won't charge. Brightness set to Auto or low, causes the charging current to go upto 850 and the % charge also increases. Given that the charger is capable of 1.5A and I have seen on occasion 1.1 A being recorded, I am not sure why it charges at constant ~850mA. Possibly due to differences in voltages. This is with Sony Charger (1.5A)
I tried it with a 2A charger, and when the screen brightness is set to max, the charging still takes place although at a very low 100mA. And normal charging shows a current of ~950mA. Which is probably why some people noticed faster charging with a 2A charger as opposed to the Sony supplied one.
In short, if you want to get the tablet to charge properly using Sony Charger, try keeping the screen brightness to low or screen off.
I must qualify the above by saying I am not an expert in chargers.. Just putting down something I noticed..