UPDATED ANSWER:
I have just noticed some OTHER irregularities with Google's Weather API. In ANY case, you need to have 8 numerical digits, in addition to the negative sign, if it applies. See the following code block (Java-based) for proper formatting. (Not the perfect algorithm, but just a quick example so that you can see the results)
lat = lat.replace(".","");
while(lat.length() < 9)
lat = lat.concat("0");
if(lat.contains("-"))
lat = lat.substring(0,9);
else
lat = lat.substring(0,8);
ORIGINAL RESPONSE:
Paul, the trick about Google's Weather API is that you don't use the coordinates as received by traditional latitude/longitude. Instead, you parse out the decimal points. Additionally, a "fun quirk" of Google's Weather API seems to be a requirement that the data come in as a 7- to 8-digit string. So, for instance, 45.5 should really be 45.50000, and -73.583 should really be -73.58300. This length of 7-8 digits does NOT seem to include the negative sign (-) in front of any negative coordinates.
So, your 45.5(0000) becomes 4550000, and your -73.583(00) becomes -7358300. So the final URL would be:
http://www.google.com/ig/api?weather=,,,4550000,-7358300
Note that again, 7-8 digits means 4550000 or 45500000 would be acceptable, as would -7358300 or -73583000.
I only found out about the 7-8 digit length when I saw your question--I tried entering the data into my weather parsing program, and found that 455,-73583 does not yield proper data.
Note that this is by my unofficial experimentation, and not by official documentation, so there may be other quirks to be discovered.