himitsuhime,
weakness on a fast is usually caused by the elimination of toxins finding their way into the bloodstream, so if you drink more water than is called for by thirst, then you will be adding to the burden of this elimination and merely delaying the process.
You could try and drink a little more water and see if this helps, but if the colour of your urine lightens from the usual darker brown, then too much water is being consumed.