Guitarists wearing picks, or other players with a heavy feel would also need to increase the action on their guitar, if they didn't want the strings to make noises as they oscillate too close to the frets. Acoustic guitar strings are nowhere near as thin as for electric, and there needs to be a compromise between thickness against comfortable use. Acoustic guitar lessons frequently cover techniques such as vibrato or bending the strings in order to raise the note a quarter tone or even more - this can be quite difficult when applying chords in proximity to the guitar nut. Heavier strings have the advantage of not moving overmuch, and also not going out of tune if pressed too hard between the frets, which can warp the string until the note varies noticeably. All thicknesses keep in tune pretty well, if used on a decent quality instrument, but lighter gauges may be affected more by temperature and humidity.
Blues guitar tabs don't normally refer to string thickness, but leaves it to the choice of the guitarist. It's useful to study the old records, and to search out old film of the players if possible, to try and find out which gauge string they used. Of course, this will have an effect on their playing style (and yours!) Light gauge strings generally go from .054 to 0.011 of an inch, and medium gauge strings range 0.056 to 0.013. It's possible to buy custom sets, such as the Blue Grass pack, which has a bass of 0.056 inch (medium gauge), but a light gauge high E string which is 0.011 or 0.012 inch.