I do monitor my weight more than 3 years already. And I do this with Libra. I know there are a lot of apps for this hot topic in the play market, but I use this one.
To be honest, I do not remember why exactly I selected Libra. But it works for me for years, so it was a good choice. My usage is very straight forward: I write down my weight daily (mostly daily) and check progress/regress. No social sharing, no diet plans - nothing, but monitoring and forecast. And Libra does this for me.