Did we always know that eating more was what made you fat? Is that just obvious, or is it something that humanity wasn't aware of?

The kinds of cheese that are most esteemed at Rome, where the various good things of all nations are to be judged of by comparison, are those which come from the provinces of Nemausus, and more especially the villages there of Lesura and Gabalis...and from the frontiers of Etruria and Liguria those of Luna, remarkable for their vast size, a single cheese weighing as much as a thousand pounds.

(Pliny, Natural History 11.97)

Oh! I'm sorry, you were asking about whether people in the past thought food could make one fat, not the tastiest ways to get there. In which case:

The size of the body is increased by eating sweet and fatty substances, as well as by drinking, while, on the other hand, it is diminished by eating dry, acrid, or cold substances, and by abstaining from drink.

(Pliny, Natural History 11.118)

"Since the dawn of time" is a little hard to answer from the historical record, and I'm definitely not an expert in ancient/medieval history of every civilization in the world. However, there are a few points I want to highlight that, I argue, demonstrate various people's understanding of the connection between consuming calories and gaining weight even if they are not so explicit as our friend Pliny.

First and most obviously are the medical/proto-scientific texts discussing obesity, its causes, and its cures. Pliny is hardly unique in the Roman world for his identification of overconsumption of food causing people to gain weight--nor in his cures. In Galen's Hygiene and The Method of Medicine, he prescribes a mixture of controlled diet, exercise (!), and medicine to treat obesity, and even records his own experience:

Now, I have made any sufficiently stout patient moderately thin in a short time by compelling him to do rapid running, then wiping off his perspiration with very soft or very rough muslin, and then massaging him maximally with diaphoretic inunctions, which the younger doctors customarily call restoratives, and after such massage leading him to the bath, after which I did not give him nourishment immediately, but bade him rest for a while or do something to which he was accustomed, then led him to the second bath and then gave him abundant food of little nourishment, so as to fill him up but distribute little of it to the entire body.

So Galen also seems to support quick weight reduction by water (sweat) loss ("diaphoretic inunctions"), but this somewhat of an illusion. He's thinking about excessive fluids in the body overall being harmful; purging bodily fluids even beyond bloodletting (blowing one's nose, enemas, here sweating) was a stock medical treatment in classical and medieval European medicine.

Beyond that, however, both the distinction between calorie dense food and so-called "volume eating" is evident. Galen also builds in a period of time where the person must not eat, limiting overall consumption.

Although a lot of texts stress medicines as a treatment, we should perhaps keep in mind 11th century Spanish Jewish doctor Hasdai ibn Shaprut's treatment of prince Sancho's obesity here. The main method was an elixir called theriac that the prince was to drink...but the key was Hasdai stitching his lips together so he couldn't eat but only drink (and only the theriac; no premodern Steak n' Shake malts for Sancho). (Unfortunately, the major secondary source on this case is in Portuguese, which I cannot even pretend to read, so I have no further information.)

Second, early and medieval philosophical as well as medical systems in the classical Mediterranean world and China all find various ways--according to their internal principles--to stress the importance of moderation in diet. Whether it's the sin of gluttony, or the vice of excess in food paralleling excess in sex and politics, or additional fat caused by the swelling of food converted to the humour of blood, or an imbalance in the elements: a disordered diet threatens or ruins one's health.

Third: well, medieval Christian Europe is...not exactly known...for its medical wisdom or effectiveness. (Muslim doctors who encountered Frankish "medicine" during the First Crusade were horrified by its barbarity). And yet even non-physician western writers recognize a connection between diet and obesity. Georges Vigarello in Metamorphoses of Fat is more concerned with attitudes towards fat people in terms of his analysis. However, his examples from high medieval French literature indicate multiple authors drew connections between eating too much and obesity--the Orleans clerics in Bourgeoise d'Orliens, the speaker in the Conte d'Arras. These are fabliaux, humorous and profane poems. While "popular" audience might not mean everyone in Latin society, clearly the comments in them need to ring true with an audience of non-Latinate, non-university educated, non-medical practitioners listeners.

Hopefully we can hear from people with knowledge of traditions beyond the Mediterranean and China, or even more familiarity with the history of Chinese science than having read Joseph Needham's work. However, what I've covered here seems to indicate a sizeable premodern awareness of the connection between eating too much food and weighing what was, by the same accounts, too much.