Yep I wouldn't worry about putting weight on from eating watermelon, there are fruits like cherries and grapes which have far higher levels of sugar. Even they won't make you put on weight unless you are gorging on them!
Watermelon won't make you gain weight if you eat it in moderation. It is a fruit though, and contains sugars. Excess consumption of sugars will convert to weight gain if you aren't burning it. So yes you could eat enough watermelon to put on weight, but I wouldn't worry too much about it.
There are probably even more sugar laiden fruits out there that would put weight on your quicker than the humble watermelon.