re: Do some credit card companies give credit line increases only to those with heavy usage?

You need to ask for an increase every 6 months.

My capital one, discover, and citibank have all given me increases when I request them every 6 months. It doesnt effect your credit, count as inquiry, etc. Most of them you can request an increase within their app or on their website. Takes just a minute or two.

If you are denied it'll just say try again later basically.

My utilization is usually reported around 1% because I pay them off several times a month.

Now you may eventually top out, but it shouldnt be at 6-8k.