I've noticed that in many cultural depictions of mythological monsters and the heroes who slew them, the heroes tend to be just as big physically, or in some cases even bigger than the monsters. Yet today, we often imagine these monsters as massive behemoths. When did we begin to think of monsters as huge?
In folk tradition, the size of monsters (and other supernatural beings including those often referred to as "gods") can be quite elastic. What is enormous can become smaller and what is human-sized can become enormous. Your perception of older equaling smaller isn't entirely accurate.
Some monsters - the Old Norse Jörmungandr also known as the Midgard Serpent or World Serpent, for example - were consistently regarded as enormous. In other stories, giants could appear human-sized, with the hero often marrying the giant's daughter. At other times, the giant can assume much larger dimensions. It all depends on the demand of the story, but it is in keeping with this idea of elasticity.
Key to traditional stories about monsters is the ability of the hero to fight effectively them - and win. A hero seeking to defeat Godzilla or King Kong by the force of his arms obviously can't be accomplished, but this is an expression of modern cinema and how it has exaggerated the size of at least some monsters.
Perhaps with this, we see something of the transition you are perceiving: traditional monsters tend not to be overwhelmingly large (except when they are!), while monsters of cinema are often enormous. Consider, for example, Tolkien's drawing of Smaug and Bilbo from what I believe is the 1930s (a Tolkien expert can help with the date). The dragon, compared with the diminutive Bilbo, is simply not that large. In the recent film adaptation, Smaug has become enormous, well beyond the size Tolkien imagined.
Heights and measurements more generally are hard to find and accurately translate in such old and varied myths. I'm not sure about the monsters getting bigger, but the heroes did get smaller.
Gilgamesh is described as being 11 cubits tall, 17-18 .
Achilles's height is not given in the Iliad, but the spears he and others use are described as about twice the length of normal spears, implying giant size.
Pythagoras is said to have calculated Heracles to be quite tall.
Characters from the Mahabharata are described as very large.
Fionn Mac Cumhaill of Celtic legend is described as a giant.
I'd be curious to see if anyone has other examples
