How can I paint consistently coloured lines with acrylic paint?
In my experiments so far I am having to go over each line several times to stop the background colour from showing through the acrylic. Even when the background is only white.


This is probably caused by the quality of your paint. Pigments are usually the most expensive ingredient in any paint, so the cheaper the paint, the less pigments are in it. In order to cover your background color you need to create a layer of pigments over it. If your paint doesn't contain enough pigments, that can only be achieved by putting several layers of paint over each other. 

There are usually 3 categories of paint:


Hobby quality: Very cheap, full of fillers and almost no pigment at all. Mixing colors is a gamble at best and impossible at worst. Useless for any crafting project. These can be found in dollar stores and similar shops that don't usually have art supplies.
College / art student quality: Good price-performance-ratio with acceptable amount of pigments. They're often offered in a wide variety of colors that usually mix well. These are best fit for crafting projects and can be found in most craft shops and some DIY or construction stores.
Artist quality: Most expensive but usually contain the most (and purest) pigments and least additives. They're often thicker in consistency than collage quality paints and some very special pigments (like ground up semi-precious stones) may only be offered in artist quality paints. Use these when you need absolute coverage of any color in small areas (like miniature painting) or when you need consistent coloration despite extreme dilution of the paint.