Another question, what's the size of the bundle using Qt?
I never got Qt4 working with Mac. Qt5 widgetset does not include support for Qt5's Web browser control.
The QtWebView.framework (64 bit) is the whopper in the bunch, with a 32MB footprint. QtGui.framework is next at 13.5 MB. The rest are fairly modest in size.
Microsoft's Remote Desktop app on Mac uses Qt4, but it only includes the Qt4 libs it needs (Core, Gui, Network, Xml). QGIS on Mac also uses Qt4 and includes all of the Qt frameworks, but since the QGIS.app footprint is 640MB, QtWebView's 32MB is only, what, 5% of the app footprint and so doesn't add much weight.