Well the heavyness in engine can be due to many issues. You can take the ride to some good mechanic. Where are you living now a days? If you are in Islamabad, try meeting Mr. Shah at Toyota capital motors, Potohar road, I-9, Islamabad. Do not go to their headquarters. I am trying to find a better place. Do update use if you find a better one.
As far as the CAT is concerned, yes, it can be a culprit. But, it's better to get other things checked first. like throttle body cleaning, plugs, filters, sensors blah blah etc.
Also check the quality of fuel you are getting. Sensitive engines respond very abruptly to fuel quality.
You can get your CVT Trans Fluid changed from the same place as I have mentioned. But do not forget to take with you all the required things. For example CVTi Fluid box gas kit. Normally they do not have such things, but if they have them, they give it at 3x price.
Also post the same question in vitz fan club thread.