I went through Bais Yaakov and heard many classes on Tzniyus from very frum Rebbetzins and NEVER did I hear anything about a requirement for loose fitting sleeves!
As long as the elbow was covered – that is what we were told the Halacha is. I for one think it is great that shells are now worn under clothing. There are many people used to wear short sleeves or low cut shirts and and now that wearing a shell has become the norm – their arms and neck lines are covered more than they have been in the past.
Let’s be grateful for this idea and how it has caught on.
That being said – the layer on top should not be very tight or it defeats the purpose.