When you download whatsapp you put in your mobile number, it will then send a text to verify that this number is correct (if I remember right it automatically realises that the phone had the message with the code and registered straight off, if I'm wrong then a code is text and put it in the WhatsApp app and finish registration).
WhatsApp also syncs up to your Google Drive account for the backup restore every night (also if you do it manually). I have just had a look on my Drive account and can't see any files there but it definately restored my messages from it when I flashed my last ROM.
Also, for the last month or two WhatsApp has finally embraced end to end encryption, what version of WhatsApp are you using? Do you know if your version has this capability?
I can't figure out how someone can see your messages unless you are originally registered with their number? One of my friends when he changed numbers was still using his old WhatsApp number somehow...not entirely sure how he managed this but he recently changed his phone (kept same said number) but then was using his new number WhatsApp, perhaps there is a loop there if you have changed your number. Open WhatsApp, hit the three dot menu top right, sewttings and click your name/picture. Is the number there your current number you are using?
