If you want ease of implementation, value for money, and good accuracy - then a cheap commercial 2 kg scales interfaced by whatever means is possible is liable to seve you well.
You can buy load cells and instrumentation amplifiers and roll your own, but the Chinese already make just what you want by the millions at a price which is liable to be far less than you can buy the parts for new.
The best (and in some cases also the cheapest) kitchen scales use a "real" load cell with 4 strain gauges in a bridge plus hopefully a 5th temperature compensating strain gauge (places on the load cell where stress/strain is caused only by temperature changes. The photo below shows a typical load cell used in low cost scales.
These can be converted to "hanging" operation either by removing the load cell from the scales body and custom mounting it (not very hard)
or by placing the scales on a beam and using a "question mark" shaped stiff wire to convey the force (weight) out around the scale body and onto the pan. I use a similar arrangement with the scales described below to suspend objects for weighing in an out of water for 'Archimedes' density measurements with good success.
Performance oc cheap kitchen scales varies from not-overly-marvellous through to unbelievably superb.I bought some end of line 2 kg kitchen scales here a few years ago for about $10 each, that were so good that I went back and bought the rest that were available - about 10 sets.
Mine looked very like these. Similar appearance no guarantee.
These are now about 'used up' and hopefully some equally good and cheap ones will turn up shortly.
Factors which relate are accuracy, linearity, repeatability and temperature independence. The first 3 are close travelling companions but not identical.
Obtain several hundred one and two cent coins. These will probably weigh close to 1.000 gram and 2.000 gram each. If not that then some other fixed mass. This is partially so banks can check amounts by weighing. They are amongst the best value for money calibration wights you can but. Make a few larger test weights by using eg coins to calibrate them. Say 100 200 400 800 gram would be easy. These can be made out of almost anything stable. Even eg plastic screwtop jars with water in - as long as they are airtight.
My scales would track linearly for any number of coins aded or removed and whether removed or added one by one or N at a time. Superb. Some scales are not so good.
Some scales are poorly temperature compensated. Mine can have a hairdrier waved over them on high until they are toasty hot (50C plus) with little of no display deviation. Superb.
Once you have found ones which are accurate enough for you, you nee to interface them to the Arduino. Most will have an anlog voltage(amplified strain gauge signal) which is converted to digital by the display controller. Signal level should be in the volt or few range - easy for an Arduino ADC to measure.
If you can't get at the analog signal you may be able to access the controller at the digital stage. Long ago people have gone so far as decoding 7 segmont multiplexed display signals for processor interface - but if it's that hard then finding ones with analog signal access would beeasier.
Some may use a V to F (Voltage to frequent) converter. These are easy to read by either pulse counting in finite time or by seeing how long it takes to make N clock cycles.
Sounds not too difficult to do what you are proposing, most digital scales use 1, 2 or 4 strain gauges in a Wheatstone bridge configuration to form a load cell.
This load cell will output a small differential signal which is read by an Instrumentation Amplifier (InAmp) to amplify and output a single ended signal that can be easily read by an ADC.
So if you have a digital scale, it's just a question of hacking it and tapping this signal to be read by your PIC, Arduino, etc, to be used as you like (send to PC, display...)
As far as I'm aware the R-Pi doesn't have analog inputs available as "standard", and it sounds like complete overkill for this anyway (unless you are using the R-Pi in place of a PC or something)
Best Answer
Here is one way to avoid load cells, bridges and all that with something possibly easier. Since you have a way to mechanically support your hive (Which sounds huge! Mine are not near that heavy even when three boxes full).
How about a simple balance and a water tank on the other arm? Pump water in or out to get balance. There are a lot of nice ways to measure depth of water in a container. You can also continuously fill till balanced then measure contents as it empties. A dump bucket as used in rain gauges could work for both in and out.
Compression of a spring with or without a lever is also good. Have you looked at the load cells that you hang something from?
Personally I like measuring ml of water to get grams - sealed of course or your bees will keep moving it into the hive :-)