Hi,
I'm not sure what you mean by "product overview" ? Supposing we're still talking about the products listing, then the price displayed is depends on that "which price" setting I was talking about.
If you select "cheapest" there (which is the default), then it's the cheapest price that will appear. If you have a product with variants: 500g / 1kg / 2kg, then the 500g variant will normally be the cheapest, and you should see that price on the listing, and if you have a product with variants 1kg / 2kg / 5kg, then it will be the price of the 1kg variant.
But as you said, it's not the price of the default variant displayed, it's the cheapest price, regardless of the variant.
If you want the system to auto select the price to be displayed to always use the 1kg variant, then there is no option for that.
In that case, it would actually require quite a bit of code customizing in the product / listing_price.php view file to load all the variants and their prices for the current product in the listing and then select the one you want to use for the display before displaying it.
So it's possible but definitely not easy.
A way simpler solution would be to enter the price you want to appear in the main product. That way, the system will automatically use the price of the main product on the listing, regardless of the prices of the variants.