Whoa...the Sigma weights 2.6kg? Are you out of your mind? You're going to carry that boat anchor everywhere you go for two months? Haven't you heard of carry-on weight limits? Unless you have a specific use in mind or aren't moving around much, I'd consider something else. Common sense says to take somethng smaller and lighter.
Also, not sure what your plans are, but if they involve typical tourist things 120-300 might not be a focal length that you'll use much. Whereas the 55-250 is a good supplement to a wider lens. I don't know about IQ of the 55-250. If you're concerned maybe consider a 50mm or 85mm? (Of course, if you're there to photograph wildlife, pleawse ignore everything I've said.)
On the other query, the chances of having gear stolen is low, but it does happen. Make sure your travel insurance covers it with minimal excess and then, apart from the inconvenience, its one less thing to lose sleep over. Look at ways to back up memory cards. I typically travel with a laptop and HDD for work anyway - but this adds to the weight. (When she's not looking, I drop the HDD in my wife's handbag for safe keeping.) And I try to upload favourite photos to smugmug whenever I can.