There is no definitive answer to this question as the average weight of household goods can vary greatly depending on the types and quantities of items involved. However, a rough estimate would put the average weight of household goods at around 1-2 tonnes. This includes both furniture and appliances, with larger and heavier items such as refrigerators and washing machines obviously contributing more to the total weight.
Of course, there will be considerable variation from home to home, and even within individual homes as different rooms will contain different types and quantities of belongings. A family home with young children is likely to have considerably more (and often heavier) items than a single person's apartment, for example.
In general terms though, 1-2 tonnes would be a reasonable estimate for the average weight of household goods.