Because the properties of soft materials emerge from the physics of the constituent polymers, we are motivated to characterize chain molecules at a fundamental level. We build upon the magnetic tweezers single-molecule manipulation technique, which involves measuring the distance between the ends of a polymer in real time and with nanometer precision while applying stable magnetic stretching forces in the piconewton range. Here we demonstrate new applications of this technique, specifically by measuring the interactions between a polymer and the surrounding solvent. First, through low-force elastic measurements, we determine a range of fundamental parameters that quantify solvent quality and chain structure. We present a force-solvent phase diagram to summarize these parameters and our experimental data, and discuss where PEG, DNA, RNA, and proteins fit into the diagram. The unstructured and structured states of a biomolecule reside at opposite ends of the diagram, indicating that folding is accompanied by a change in the character of the solvent. We therefore chose to investigate the local solvent change that occurs when a charged biomolecule folds. We present a thermodynamic framework for measuring the uptake of counterions that accompanies nucleic acid folding. Our measurements of a simple DNA hairpin identify potential shortcomings in thermodynamic parameters of MFOLD, the most widely used predictive software for nucleic acids. Finally, we present a variety of polymer immobilization schemes, achieve low-noise measurements with a strong magnet design, identify new assays, and provide technical guidance that may be useful to those interested in pursuing future magnetic tweezers experiments.