Weight (and the tyres)are the important issues when you buy a bike.
You can try it by yourself:
Start at bellevue with your citybike and climb up to the ETH(write down the time you need).
Now , take a roadbike(with less then 8 KG weight itself) and climb again from
bellevue to the ETH(write down again the time).
A good bike cost(a lot of) money and will not be sold for 250 sfr, the components are well worth the money on a bike what is more expensive(more fun , last longer).
But it is your decision how much money you will spend.