Should be well known fact but brains washing... oops marketing, is powerful.
Found a irrefutable table: Same manufacturer, same model rims in different sizes with their weights.
https://www.vorswheels.com/pages/vors-wheel-weight
15 x 8 12.5 lbs.
18 x 8 21.2 lbs.
The tyres hardly get heavier/lighter if at all. The sidewall reduction can be more than offset by the larger diameter bead.
Actually tyre models can vary significantly and are the worst culprits for contributing to rotating inertia. Trouble with larger diameters is a greater impact on rotating inertia.
My experience is Goodyear make the lightest tyres for size equivalence, also meaning a more forgiving ride even with lower profiles.
Similarly with the improved quality of budget tyres made in factories also supplying premium brands in low cost markets,, you an get some excellent tyres for less money which tend to be a bit lighter and softer as part of their lower price and performance ratings. I brand I've gotten to trust is Ling Long, made in the Yokohama factory in South Asia somewhere, Japanese process and material quality passed on to low cost manufacturers. For my daily cars the performance and comfortable exceed requirements and I've always been pleased with them and for 1/3-1/2 the price and a somewhat marginally higher wear rate they always served me well.
But back to topic, wheels and manufacturing methods can have significant effects, especially since the majority of wheel mass is in the rim, potentially some in the spokes also. Japanese manufacturers developed a spun cast process first, which rather than simply pouring hot metal into the cast rotates the cast also forcing the metal out into the cast well and meaning better grain structure and therefore stronger and lighter cast wheels without the cost of forging. 8)
Ultimately though for strength to weight ratio forged wheels are the best solution, the manufacturing process yields strongest metallic properties meaning less material required for the strength of wheels therefore less weight. And typically requires further machining allowing the manufacturer to minimise material where it is not required such as between the bead rims which would typically require more breadth to allow flow of material during forging or casting. But none of these extra benefits are for free ;)