Dissolving collagen in water: Why does the weighing scale reading fall?
Because collagen does not react with water and you say, no (measurable) evaporation of water is evident, there are only two options as to what is happening:


Matter is converted into energy:
If virtually no evaporation or spillage took place, and your scale is working properly, this is what must have happened. Using the formula of mass-energy equivalence $E=mc^2$ (E = energy, m = mass, c = speed of light in a vacuum) we can calculate the amount of energy that should result from a "loss" of 2 grams:
$$ E = 0.002~kg\cdot(2.998\cdot10^8~m/s)^2 $$
$$ E = 0.002~kg\cdot8.988\cdot10^{16}~m^2/s^2 $$
$$ E = 1.798\cdot10^{14} (kg~m^2)/s^2 = 1.798\cdot10^{14}~J$$
so... that would be a LOT of energy.
Your scale is not working as intended.


I'd go with option 2.

Now on a serious note: We do have a scale (precision of 0.0001 g) in our lab that occasionally has the same problems. Sometimes I would measure an empty reaction flask and it would be fine but some other time I could watch the measured weight drop by the second, "losing" up to 100 mg. The scale was checked by a professional but he could not find anything wrong with it.

My advice is: try another scale, see if the problem persists.