Are there accurate meat scales which interface easily with a computer?

What would a network-attached scale even do? You'd have to configure it to report to something, or have something else poll for it (and then you'd still have to configure it, either via DHCP, BOOTP or similar to set its IP address). It'd be a security nightmare, as it'd be like a network attached medical device (or old printer) that never gets updates to deal with security vulnerabilities. Some sort of a serial connection like RS-232 or USB is just plain safer in this situation.

... and there are plenty of USB digital scales, as they're used by companies to weight packages & print out postage.

The only reason to not go with USB might be distance limitations (5m for USB 2), but you can get USB over Cat5 'extenders'. (which would then meet your 'cat5' cable requirement ... but you can also get DB9 (or DB25) to RJ45 adaptors, if you just want to run 232 over cat5)

(I'm a programmer/sysadmin at a US government agency so it's possible that my security concerns are a little higher than most other people's. Even if you keep it on an isolated network to only talk to the terminal, odds are that the terminal is going to need to be updated at some point, and you risk it getting infected. Even if they exist, it's just not worth the trouble. And yes, I do know about the attacks via USB devices)

If you have an RS232 scale you have a couple of very decent options for getting the data out of it. You could get an RS232 to USB adapter and write a script of some kind to request and pull the data - probably the easiest option - however it would not have network access, just access from the wired computer. If you genuinely want it to be on the LAN then I'd use a LAN or WIFI enabled Arduino to interpret the RS232 data and convert it to whatever format you want. You could have it do a HTTP push to a server or have it run its own web server so the data could be pulled.

I haven't looked but there probably isn't a networked meat scale. Most equipment like this is attached to a cheap computer that can packetize the data coming off the serial connection. If you have an old pentium computer you just haven't thrown away yet, you could probably roll your own Linux system and write an app in ASM or C to just transport input from the serial port and drop it on the lan via either SNMP or SMTP or other messaging mechanism or even drop it on a mounted share drive.

HOWEVER, this question is probably more appropriate for one of the tech forums such as electrical engineering g, Unix, or programming.

So what you want is something that can attach to a network, weigh your duck, tell someone something about the weight of the duck, and have it all be above board so that you don't have to be afraid of fleecing your customers?

The only thing that I have personally used and have had any experience with that fits your bill is Digis systems.

This seems like a good fit for what you want

While I have not used that specific solution myself, I have used their weight + wrap + label stuff before, and it works as advertised, more or less. Never had it die on me either.

I'm sure that there are competitors to digi, but I have only used their stuff professionally, so I cannot comment on them.

Hope this helps.