Regioregular poly(3-dodecylthiophene) films self-organized on highly oriented pyrolytic graphite have been investigated by scanning tunneling microscopy and two-dimensional scanning tunneling spectroscopy (STS). Simulated spectra in very good agreement with the experimental data have been obtained by a method combining ab initio and semiempirical approaches, which allows a careful discussion of the polymer electronic states. From the experimental data, with the support of modeling, it is shown that the STS spectra give a direct access to the polymer semiconducting band gap without noticeable charge-transfer effects from the substrate. Spectroscopic images are achieved at the single chain scale, which allows scrutinizing the electronic consequences of chain folds and π-stacking effects through spectroscopic contrasts. While chain folds do not locally increase the polymer band gap more than a few tens of millielectonvolt, a striking widening of the STS conductance gap is observed in the case of electronic tunneling through two interacting polymer layers. Scenarios based on nonplanar configuration of thiophene cycles within the second layer or variations of the charge screening effects are proposed to explain this phenomenon.