To create a model that incorporates different slopes for different groups, create indicator variables for the groups. Multiply the indicator columns by the body weight column. Then regress Liver weight on Body Weight and the body weight times the indicator for two groups. That gives an interaction model between body weight and group but allows all three groups to be analyzed simultaneously.
You also need to deal with at least one really bad outlier.
Liver_weight Body_weight Group 15.96 419 1 13.78 419 1 16.33 438 1 13.25 408 1 14.61 397 1 23.23 580 1 17.74 518 1 16.12 429 1 15.77 464 1 16.84 503 1 28.66 454 2 17.77 453 2 14.55 475 2 15.06 464 2 15.61 474 2 13.27 423 2 13.26 400 2 12.98 428 2 14.93 455 2 16.68 490 2 20.69 557 3 15.39 462 3 14.87 427 3 16.44 438 3 16.66 457 3 15.80 458 3 19.37 528 3 18.27 523 3 19.15 530 3 16.51 516 3