Context. Despite their variety of scales throughout the interstellar medium, filaments in nearby low-mass clouds appear to have a characteristic width of similar to 0.1 pc from the analysis of Herschel observations. The validity and origin of this characteristic width, however, has been a matter of intense discussions during the last decade. Aims. We made use of the EMERGE Early ALMA Survey comprising seven targets among low- (OMC-4 South, NGC 2023), intermediate- (OMC-2, OMC-3, LDN 1641N), and high-mass (OMC-1, Flame Nebula) star-forming regions in Orion, which include different physical conditions, star formation histories, mass, and density regimes. All targets were homogeneously surveyed at high- spatial resolution (4.5 '' or similar to 2000 au) in N2H+ (1-0) using a dedicated series of ALMA+IRAM-30m observations, and previous works identified a total of 152 fibers throughout this sample. Here, we aim to characterise the variation in the fiber widths under the different conditions explored by this survey. Methods. We characterised the column density and temperature radial profiles of fibers using the automatic fitting routine FilChap, and systematically quantified its main physical properties (i.e. peak column density, width, and temperature gradient). Results. The Orion fibers show a departure from the isothermal condition with significant outward temperature gradients with del T-K > 30 K pc(-1) . The presence of such temperature gradients suggests a change in the equation of state for fibers. By fitting their radial profiles, we report a median full width at half maximum (FWHM) of similar to 0.05 pc for the Orion fibers, with a corresponding median aspect ratio of similar to 2. Along with their median, the FWHM values for individual cuts are consistently below the proposed characteristic width of 0.1 pc. More relevantly, we observe a systematic variation in these fiber FWHM between different regions in our sample. We also find a direct inverse dependence of the fiber FWHM on their central column density, N-0 , above greater than or similar to 10(22) cm(-2) , which agrees with the expected N-0 - FWHM anti-correlation predicted in previous theoretical studies. Conclusions. Our homogeneous analysis returns the first observational evidence of an intrinsic and systematic variation in the fiber widths across different star-forming regions. While sharing comparable mass, length, and kinematic properties in all of our targets, fibers appear to adjust their FWHM to their density and to the pressure in their host environment.