The weak interaction is the only fundamental interaction in nature that violates parity symmetry. Parity-violation produces asymmetric outcomes in mirror image experiments. The high-precision asymmetry measurements, using electrons with rapidly flipping polarization as probes, have extraordinary scientific reach across various subfields. PREX-2 and MOLLER are two such experiments that can only be conducted at the state-of-the-art Thomas Jefferson National Accelerator Facility. The asymmetries (A_PV) measured at PREX-2 and MOLLER kinematics (Q^2), can help to estimate the density distributions in neutron-rich matter and search for Physics Beyond the Standard Model respectively. PREX-2 was conducted by scattering a longitudinally polarized 953 MeV electron beam elastically from 208Pb at a ~ 5 degree scattering angle. The measured asymmetry was A_PV = 550±16 [stat.]±8 [sys.] ppb at average Q^2 = 0.00616 GeV^2. Together with PREX-1, it imposes robust constraints on the interior baryon density (0.1480±0.0036 [exp.]±0.0013 [theo.] fm^−3) and the neutron skin (0.283±0.071 fm) of 208Pb. Model correlations between the neutron skin and the nuclear symmetry pressure indicate a stiff symmetry energy near the nuclear saturation density. Together with neutron star observations, it enhances the understanding of exotic matter states. In contrast to PREX-2, MOLLER will operate with an 11 GeV longitudinally polarized electron beam as the flagship experiment utilizing the 12 GeV upgrade at Jefferson Lab. The electrons will be scattered from atomic electrons in a liquid hydrogen target and the scattered electrons will be guided by a novel spectrometer with full azimuthal coverage to an array of quartz Cerenkov detectors. The asymmetry and consequently the weak charge of the electron will be measured to a precision of 2.4% at average Q^2 = 0.0056 GeV^2. The value of the electroweak mixing angle derived from the above measurement can be compared to the Standard Model prediction in search of a deviation. MOLLER is sensitive to new physics in the MeV to multi-TeV range. This dissertation details the PREX-2 measurement and the current design status of MOLLER, highlighting my contributions towards PREX-2 data analysis and optimization of MOLLER experimental subsystems.