Accurately quantifying carbon source-sink changes resulting from carbonate weathering under the influence of anthropogenic acids (HNO₃ and H₂SO₄) in karst rivers of northern China is of great practical significance for supporting China's "Carbon Peak and Carbon Neutrality" goals. This study focuses on the Yufu River (YFR), a typical karst river in northern China, based on a surface water survey conducted during the dry season of 2019. By integrating hydrogeochemical and isotopic tracer methods (δ¹⁵N_NO3, δ¹⁵N_NH4, δ¹⁸O_NO3 and δ¹³C_DIC) with the Bayesian isotope mixing model (Simmr) and hydrochemical mass balance (forward modeling), we quantitatively identified the sources of nitrate and evaluated the roles of H₂CO₃, HNO₃, and H₂SO₄ in carbonate weathering and CO₂ sequestration. The Simmr model constrained by hydrochemical parameters and dual nitrogen isotopic data revealed that the main sources of nitrate in the Yufu River catchment were soil nitrogen (34.6%-39.3%) and ammonium fertilizer (27.7%-39.9%), followed by nitrate fertilizer (9.5%-16.7%), with relatively lower contributions from sewage and manure (7.1%-12%) and atmospheric deposition (4.4%-7.5%). The ion ratios and δ¹³C_DIC values indicated that in addition to natural carbonic acid, externally derived acids such as HNO₃ and H₂SO₄ from anthropogenic activities significantly participated in carbonate weathering. Hydrochemical mass balance calculations showed that CO₂consumption followed the order: Jinyangchuan (JYC)>YFR main stream>Jinxiuchuan (JXC)>Erxian River (EXR). The amounts of CO₂ released by sulfuric acid and nitric acid-mediated carbonate weathering decreased in the sequences EXR>JXC>JYC>YFR and EXR>JXC>YFR>JYC, respectively, which may be related to variations in agricultural fertilizer intensity across sub-basins. Notably, the net CO₂ consumption rates across four monitoring sites exhibited significant spatial differences: JYC (+0.26 mmol/L), YFR (+0.01 mmol/L), JXC (-0.81 mmol/L), and EXR (-2.13 mmol/L). Among these, the JYC demonstrated a clear karst carbon sink effect with net CO₂ consumption, YFR was near carbon neutrality with approximately balanced CO₂ flux, while JXC and EXR functioned as net carbon sources releasing CO₂ into the atmosphere. These spatial variations reflect the complexity of hydrogeochemical processes and their influence on the carbon cycle across the watershed. The findings highlight that intensive application of reduced nitrogen and sulfur fertilizers in agriculture leads to significant anthropogenic acid involvement in carbonate weathering, which is a key factor weakening the riverine carbon sink effect in northern China's karst regions. This study provides an important scientific basis for constructing river carbon cycle models and accurately assessing watershed carbon sinks in northern China and other temperate karst areas.