high density concrete typically would have a density of around 3.6T/m3 due to aggregate type. Not sure what conclusions you can draw from this for use of air entrainment. I think that the mix design will have significant development and testing probably using higher levels of resources than available on a internet forum.
I thought that air entrainment was to protect concrete in freeze and thaw cylcles. Is that what you need? Is there another benifit you are trying to get from the air entrainment?
The intent of Heavyweight concrete is higher density. Air entrainment decreases density. While air entrainment increases workability, you can achieve the same result with other admixtures. Doesn't seem like much of a point for using it here.
Heavyweight concrete is often used on submarine pipelines to reduce in-air weight, but keep the same submerged weight. As Ron says there is not much point in using air entrainment, especially as the resulting densities are variable.
The heavy aggregate is often haematite which makes the concrete red in colour.