I guess if software and hardware setup like what Dan suggest has a voice synthesizer to repeat the data, all that is needed is a radio.
Now that is two too many IF's.
The second part is it legal to broadcast continuous on VHF aviation freqs Unofficially. I brief study of the AWOS subject it looks like there are regulations and specification for the official ones. I understand you want it for your own personal use, but what does an official one cost. I am guessing a lot and more than you want to spend.
I would think it would be nice if you did get a general weather station hardware/software that could synthesize voice, the alternative to continuous broadcast would be like PCL lighting, several clicks would key the transmitter only for 20-30 second. I think that might get around some FAA/FCC issues. A advanced hobbyist could wire up a fancy "clapper" to key the transmit side of the radio with a relay across the mic PTT. A simple timer activated by set number clicks that shuts down after 30 seconds can be made with a few parts ($10-$20). This would help from burning the radio out and allow use of a regular com radio. Not having continuous TX might be a nice thing.
May be continuous broad cast with a low watt radio with antenna placement for only near range broadcast to the field might get around the oversight of the FAA/FCC. Keep use informed. I plan on a private field and would love to also make one.
George
PS, Here is a Voice synthesizer
http://www.rcsys.com/dt.htm
Now all you have to do is program the software to send text thru the serial ports. Some weather stations claim to have RS232 serial output? How all that might work together, who knows, but have fun researching it. Add the radio you might have a system for about a grand to $1500, Used or stripped down computer and crummy monitor, $500; weather station, $330 (Oregon scientific); pc software, $70; V. Synth, $300 and an old used com radio/antenna, $400. If you don't want to make the radio TX with radio clicks, if you are a day only airport, the radio can come on at dawn and go till dusk with a wall timer on the power supply. Another option is a simple timer/relay I could even make, to key the mic every 20 seconds on, 40 seconds off, or something like that to save the radio. Although the click activated type would still be easy, I can't wire up one from the top of my head. If you want one I can look into it. It would be easy to do with a few parts, most available at radio shack.
Just some random thoughts, but from Dan's suggestion and what I see, it looks like you could cobble together some off the shelf stuff with little cash ($1500 or less). It will not be free or with out set-up (assume you have a outbuilding and a/c power).
It would be nice to know the winds, temp, baro and even rain fall in the last few hours. ( I landed at a wet soft-field once not knowing the field was wet. Long story I would not have landed knowing the field had be dumped on that morning. I got in an out with out much problem, but besides mud, takeoff performance was hampered by field conditions and made the takeoff more sporty than I liked, lesson learned.)
Last note, you might want to casually check the FCC legality at setting up a broadcast station with the FCC. I would think the click activate one with limited transmit reply time might be a no brainier from a legal standpoint. Also I am not sure a regular COM can take 24/7 transmitting? G