Yes, you can log it on the app.
On your app dashboard go to the icon that looks like digital scales (just above sleep icon) click on it then you will see "Log Weight" in red. click on this and you can enter your details.
You don't say which app you have and as this is posted in the Surge forum rather than an app forum it's very hard to tell!
Having said that, as reported above I can do this under iOS and Windows Phone so I doubt that Android excludes the functionality. All apps should be covered here.
Mike | London, UK
Blaze, Surge, Charge 2, Charge, Flex 2 - iPad Air 2, Nokia Lumia 925 (Deceased), iPhone 6
Take a look at the Fitbit help site for further assistance and information.
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