Animated.Value does not increment properly

Say for example I want a value to animate between 0 and 1. Nothing would happen if I were to do this. I must set the initial value to >0.001 for it to actually do anything.

Environment

react-native-cli: 2.0.1
react-native: 0.61.5
System:
OS: Windows 10 10.0.18363
CPU: (12) x64 Intel(R) Xeon(R) W-2133 CPU @ 3.60GHz
Memory: 15.79 GB / 31.73 GB
Binaries:
Node: 10.16.3 - C:\Program Files\nodejs\node.EXE
Yarn: 1.22.0 - C:\Program Files (x86)\Yarn\bin\yarn.CMD
npm: 6.9.0 - C:\Program Files\nodejs\npm.CMD
npmPackages:
react: 16.9.0 => 16.9.0
react-native: ^0.61.5 => 0.61.5
react-native-windows: 0.61.0-beta.22 => 0.61.0-beta.44
Installed UWP SDKs:
10.0.17763.0
10.0.18362.0

Steps to Reproduce

Use this app code:
https://snack.expo.io/I5ZIbQtHJ

Expected Behavior

The opacity of the text shifts from 0 to 1 over the course of 1 second.

Actual Behavior

The Text element stays invisible forever. However, if I initialize mySmallAnimatedValue to any value > 0.001, it will work properly.

Additional context

Adam Gorman(adamgor)
Austin Beaulieu(aubeauli)

Start with the Snack reproduction linked in the issue and trace the Animated.Value entry point used for the opacity animation. Confirm the behavior with an initial value of 0 and verify that the text opacity reaches 1 after the one-second animation without requiring a value above 0.001.