Better scales can't harm, but in the experiments I did, it was not the weakest element.
Imagine banal scales give 0.1g accuracy in a 100g measure (laboratory scales are much better). That's already 0.1%.
The weight of the displaced air is more than 0.1% the weight of the water. Forgetting it would be worse than using banal scales.
Water expands by 200ppm/K around room temperature so 5K inaccuracy brings 0.1% too. Nothing tragic, but keep an eye on it.
And above all, how accurate is the container? Imagine 100mL as D=50mm h=50mm approximately. 0.1% demands 17µm accuracy on both dimensions.
I had turned my containers of aluminium, and then the dimensions are easily that accurate. But what if the bottle is of plastic or glass? And in the case of plastic, thermal expansion is a worry too.
Then, what defines the liquid's filling level? If a D=50mm cavity ends straight you won't estimate the filling level to 17µm. It needs to observe the stop level in a narrow neck, but then the container's shape imposes to assemble two parts, which may ruin the manufacturing's accuracy.
No wonder that, everytime possible, experimenters only compare densities of liquids, often referring to water.
If an absolute density measure is mandatory, the standard method is to plunge a metal cylinder of accurate diameter in the unknown liquid, move it down by an accurate height, and measure how much additional mass of the unknown liquid has overflown of the containing beaker. Because of capillarity, the plunger must be uniformy clean and move always down.