You need quotes around that content inside of the JSON object try and you need to quote the entire string so that spaces inside the variables don't make anything after the space get treated as a separate argument.
echo '"{"WAL\"WAL-VSX-02"02\": ["'"$TIME"'"[\"$TIME\","'"$FWK"'"\"$FWK\","'"$CON"'"]\"$CON\"]}'"
The way you had it before there were (single) quotes around several components of the string which works but if there are spaces in any of the vars then the shell parses it as separate strings. This way the whole thing is quoted so the shell will parse it as one string.