uses wininet;

...

function GetUrlSize(const URL:string):integer;//результат в байтах

var

  hSession,hFile:hInternet;

  dwBuffer:array[1..20] of char;

  dwBufferLen,dwIndex:DWORD;

begin

Result:=0;

hSession:=InternetOpen('GetUrlSize',INTERNET_OPEN_TYPE_PRECONFIG,nil,nil,0);

if Assigned(hSession) then begin

 hFile:=InternetOpenURL(hSession,PChar(URL),nil,0,INTERNET_FLAG_RELOAD,0);

 dwIndex:=0;

 dwBufferLen:=20;

 if HttpQueryInfo(hFile,HTTP_QUERY_CONTENT_LENGTH,@dwBuffer,dwBufferLen,dwIndex) then Result:=StrToInt(StrPas(@dwBuffer));

 if Assigned(hFile) then InternetCloseHandle(hFile);

 InternetCloseHandle(hsession);

end;

end;