Stroke width and color gradient are good choices, because you are dealing with ordinal data. Dotted/dashed line would not be a good choice for ordinal data.
Since you want the user to be distinguish frequent from less frequent routes, you need to choose a visual property that represents ordinal data.
Ordinal data is typically separated into natural, ordered categories, where the distances between the categories is not known -- for example small, medium, large. It is distinct from quantitative data.
In Chapter 4 of his book Designing Data Visualizations, Noah Ilinisky says:
Whether a visual property has a natural ordering is determined by
whether the mechanics of our visual system and the “software” in our
brains automatically—unintentionally—assign an order, or ranking, to
different values of that property.
For example, position has a natural ordering; shape doesn’t. Length
has a natural ordering; texture doesn’t (but pattern density does).
Line thickness or weight has a natural ordering; line style (solid,
dotted, dashed) doesn’t. Depending on the specifics of the visual
property, its natural ordering may be well suited to representing
quantitative differences (27, 33, 41), or ordinal differences (small,
medium, large, enormous).
The image attached is also taken from his book. It suggests that line weight and color saturation (gradient) are intuitive ways to encode ordinal data.
Also shown in the image, a dotted/dashed line (line pattern) would not be a good choice for ordinal data.