I visited Venice recently. In one restaurant menus were priced in grams and not per portion. So this resulted in several times bigger bill when I have originally expected. Is this type of pricing is standard in Italy or Venice?
First of all, looking at the reviews for Osteria da Nico on Tripadvisor, regrettably you fell prey to a tourist trap.
Regarding your question on pricing by weight: such is typical for foods such as meat (e.g. a steak) or especially seasonal fish but very untypical for regular courses (such as e.g. a Pizza). You can find the menu of a reputable Italian restaurant here (no affiliation) and will see that only T-bone steak and fresh fish are priced per 100g. I have encountered such pricing not only in Italy but all over the world.