Here's my test code that creates a resizible textarea:
Code:
Ext.create('Ext.form.field.TextArea', {
    renderTo: document.body,
    name: 'aaa',
    fieldLabel: 'Aaa'
});

Ext.create('Ext.resizer.Resizer', {
    target: Ext.ComponentQuery.query('[name=' + 'aaa' + ']')[0]
    , pinned: true
});
(I tried passing "resizable: true" as part of the TextArea config, but it seems to do nothing)

As soon as the handles are created, the <textarea> element becomes twice as narrow as its containing component. The reason is: the <label> and the bodyEl <div> have "display: table-cell;", but the handle divs have default display.