To be pedantic, all cars are weighed at the end of the race as this is when a car is at its lightest. Also a car weighed before the race could be interfered with to remove weight.
The water cooled brakes saga is a great example of teams will do to beat the scrutineers
http://en.wikipedia.org/wiki/FISA%E2%80 ... led_Brakes
Tyrell also used water injection to cool the engine
http://en.wikipedia.org/wiki/Tyrrell_Ra ... ontroversy
Only a random sample go to the scrutineers between Q1 and the race, and that may or may not include weighing.
All cars in Q3 are weighed. This is highlighted as a new clause in 2011 regs, but I don't have the 2010 regs to spot the difference.
A car only has to be legal once competition starts, ie Q1. A team can run anything they like in FP, provided it is safe and has been crash tested. That's how they are allowed to run with aero test kit on the car.
Similarly they could be under weight or have less than 1 litre of fuel if they wanted in FP. For example teams will run a car dry at the start of the season to test the fuel consumption.
I've uploaded a sample of the stewards reports so you can see what they test.
http://www.mediafire.com/?dg8nadvznk1mblc
Here's an extract of the regs.
F1 Sporting regs wrote:26) WEIGHING
26.1 a) During the qualifying practice session cars will be weighed as follows :
1) The FIA will install weighing equipment in the first pit garage (the FIA garage) which will be used for the weighing procedure.
2) Cars taking part in Q1 and Q2 will be selected at random to undergo the weighing procedure.
3) When signalled to do so the driver will proceed directly to the FIA garage and stop his engine.
4) The car will then be weighed with driver and the result given to the driver or a team representative in writing.
5) At the end of the qualifying session all cars which took part in Q3 will be weighed. If a driver wishes to leave his car before it is weighed he must ask the technical delegate to weigh him in order that this weight may be added to that of the car.
6) if the car is unable to reach the FIA garage under its own power it will be
placed under the exclusive control of the marshals who will take the car to be weighed.
7) a car or driver may not leave the FIA garage without the consent of the FIA technical delegate.
8 ) if a car stops on the circuit and the driver leaves the car, he must go to the FIA garage immediately on his return to the pit lane in order for his weight to be established.
b) After the race every classified car will be weighed. If a driver wishes to leave his car before it is weighed he must ask the technical delegate to weigh him in order that this weight may be added to that of the car.