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This study explores the influence of various parameters on bead profiles within the wire arc additive manufacturing (WAAM) process, specifically focusing on ER70S-6 low-carbon steel to produce thick-walled parts. The critical geometric characteristics under scrutiny are bead width (BW) and bead height (BH), with the primary goal being optimization. The research methodology incorporates the utilization of the Taguchi method, analysis of variance (ANOVA), regression modeling, and grey relational analysis (GRA) to scrutinize and enhance process parameters. The results reveal that a rise in wire feed speed (WFS) from 5 to 8 m/min and voltage (V) from 18 to 24 V leads to a substantial increase in BW, with contributions of 79.90% and 4.77%, respectively, according to ANOVA. Conversely, a rise in traverse speed (TS) from 0.3 to 0.6 m/min results in a reduction in BW by 11.90%, while the impact of gas flow rate (GFR) is relatively minor. Regarding BH, a rise in WFS within the 5–8 m/min range significantly enhances BH, with an ANOVA contribution of 17.78%. In contrast, higher voltage and TS lead to a reduction in BH, with TS exhibiting the dominant influence at 46.08%, followed by voltage at 31.13%, and WFS at 17.78%. The GFR exerts a negligible impact at 0.88%. To address the challenge of multi-objective optimization, GRA is proficiently employed, resulting in recommended process parameters for BW and BH: WFS = 8 m/min, V = 18 V, TS = 0.3 m/min, and GFR = 18 L/min. These results are robustly validated through experimental verification, affirming the accuracy of predictive models. [ABSTRACT FROM AUTHOR]