How to connect 111ager Solid State Relay with Arduino to control a 5VDC@2.1A load
If the rough specifications that are available for the relay are correct, then it is not suitable for your task.


ON the relay image on the site you quote the usable voltage range is shown as 5-220 VDC.
This stack exchange question and answer from 2014 Arduino SSR 5V DC (Mager GJ-3FA-L) indicates tat the relay is for use with 5V-220VDC and has a typically 2.5 VDC dro on the load side when on.


So - you are trying to use the relay with a voltage that is higher than the minimum allowed by the USB spec (ie 5V). Designs MUST ALWAYS use worst case specifications.

Even if it worked at USB vltages, the 2.5V drop wil make it completely unsuited to your application.

Measuring the on-voltage-drop with a meter will allow you to better determine the actual drop. 

Metallic contact relays are still, in many cases, and apparently including this one. a better solution than are SSRs. Alas.

You could make a switch that met your need using a suitable MOSFET and perhaps an optocoupler if you need good isolation.