It is said that Lavoisier and Lomonosov both discovered that the cumulated mass of reactants is conserved. My question is simple: who (and when) started weighing chemical products before and after forcing them react?
We shall never know who was first. The term "stoichiometry" was introduced by Richter in The Art of Measuring the Chemical Elements only in 1792, but the practice long predates modern chemistry. It was done by metal workers and alchemists in the centuries past, although they had few means to control for confounding factors, such as escaping gases or overlooked ingredients. Not to mention the roughness of the balances used. Forbes in On the Origin of Alchemy mentions practices of ancient alchemists like Bolos in this regard:
"Therefore, after its incubation period in Mesopotamia, alchemy with other theories came to Alexandria, the great pooling center of the Hellenistic sciences, where it was crystallized into a clear-cut doctrine by the logical-minded Greeks. This codification period starts with the "Physika" of Bolos Democritos of Mendes (200 B.C.)... It seems that Bolos and the alchemists were interested in the transmutation of matter, which they believed to be effected and indicated by the color changes produced in alloying and dyeing operations... The color change, which to these alchemists seems the proof of this transmutation, effected by dyeing, by varnishing and alloying and is quantitatively controlled in some cases by the increase of weight."
It got more precise during middle ages. Van Helmont (1577-1644) staged the following curious experiment, see History of Alchemy and Early Chemistry by Katz:
"He took 200 pounds of earth dried in an oven, and having put it into an earth en vessel and moistened it with rain water, he planted in it the trunk f a willow tree of five pounds weight; this he watered, as need required, with rain or distilled water; and to keep the neighbouring earth from getting into the vessel, he employed a plate of iron tinned over and perforated with many holes. Five years having elapsed, he took out the tree and weighed it, and (including the weight of the leaves that fell during the four autumns) he found it to weigh 169 pounds 3 ounces. And having again dried the earth it grew in, he found it only about 2 ounces short of its former weight of 200 pounds; so that 164 pounds of the roots, leaves, wood, and bark, which constituted the tree appeared to have sprung from the water alone."
Rey in 1630 published an essay On an Inquiry Into the Cause Wherefore Tin and Lead Increase in Weight on Calcination, indicating that the phenomenon was common knowledge at the time. This is the essay where he defended conservation of mass on speculative atomistic grounds, see An historical note on the conservation of mass by Whitaker. When the first scientific theory of chemistry, the phlogiston theory, was introduced by Stahl in 1667, this observation was used as an objection to it. According to Stahl, decalcination of metals amounts to liberating phlogiston contained in metal ores (calces), contrary to calces weighing more than the resulting metals. Some chemists even ascribed negative weight (buoyant effect) to phlogiston to explain the phenomenon, implicitly relying on the conservation law. Newton, who was obsessed with alchemy in his later life, measured weights meticulously, as recorded in his notebooks, see facsimile in Katz's paper, pp. 60-61.
By mid-18th century the weighing was standard practice among experimental chemists. For example, Black in Experiments upon Magnesia Alba, Quicklime and Some Other Alcaline Substances (1755) noticed that the amount of sulfuric acid required to dissolve calcined magnesia was slightly less (by 1-9%) than that required to dissolve the amount of magnesia originally heated for calcination. He also anticipated the conservation law in trying to explain the difference (quoted from Whitaker):
"As in the separation of the volatile from the fixed parts of bodies, by means of heat, a small quantity of the latter is generally raised with the former; so the air and water, originally contained in the magnesia, and afterwards dissipated by the fire, seem to have carried off a small part of the fixed earth of this substance. This is probably the reason why calcined magnesia is saturated with a quantity of acid, somewhat less than what is required to dissolve it before calcination: and the same may be assigned as one cause which hinders us from restoring the whole of its original weight, by solution and precipitation."
Similar observations can be found in Cavendish's notes. This predates Lomonosov's experiments (1756), let alone his letter to Euler (1774), where the conservation law was communicated, and Lavoisier's formulation of it (1773).