The immediate problem is that the code the Arduino uses to parse your code is poorly written and not very robust. You can get around the bug by splitting that big string up into several smaller strings - just put a pair of double quotes in the middle of it so that you get something like this:
PROGMEM String string = "<td >WIND %</td><td style='background-color: rgb(36, 184, 36)'>24%</td>"
"<td style='background-color: rgb(36, 184, 36)'>24%</td><td style='background-color: rgb(36, 184,"
" 36)'>25%</td><td style='background-color: rgb(36, 184, 36)'>25%</td><td style='background-color:"
" rgb(36, 184, 36)'>26%</td><td style='background-color: rgb(36, 184, 36)'>26%</td><td style='backg"
"round-color: rgb(36, 184, 36)'>23%</td><td style='background-color: #FFCC32'>18%</td><td style='ba"
"ckground-color: #FFCC32'>14%</td><td style='background-color: #FFCC32'>13%</td><td style='backgrou"
"nd-color: #FFCC32'>13%</td><td style='background-color: #FFCC32'>13%</td><td style='background-col"
"or: #FFCC32'>14%</td><td style='background-color: #FFCC32'>15%</td><td style='background-color: #F"
"FCC32'>15%</td><td style='background-color: #FFCC32'>15%</td><td style='background-color: #FFCC32'"
">15%</td><td style='background-color: #FFCC32'>14%</td><td style='background-color: #FFCC32'>13%</t"
"d><td style='background-color: #FFCC32'>12%</td><td style='background-color: #FFCC32'>11%</td><td "
"style='background-color: #FFCC32'>11%</td><td style='background-color: #FFCC32'>13%</td><td style="
"'background-color: #FFCC32'>12%</td>";
All the other comments about ill-advised use of the String class and problems dealing with huge strings in RAM apply too and I'm sure you will need to address those before you sketch will work correctly, but splitting the string up should get you past this silly IDE bug. Judging by the error message I get from 1.5.2 I suspect the limit is 1024 characters in a string, but I haven't confirmed that and it may not be the same for all IDE versions anyway.