The measurement should be taken at the heart girth.  This is just behind front legs up to withers, but not including the shoulder blades. It should be snug, but not overly tight. These are reasonable estimates of the weight of standard dairy goats (not for pygmies or nigerian dwarves).  If done properly, in research these have been proven to be accurate within 5 pounds, plus/minus.

 

INCHES    CENTIMETERS   POUNDS     KILOGRAMS  

10 ¾          27.3                 5                2.27

11 ¼         28.6                 5 1/2         2.49

11 ¾         29.9                 6               2.73

12 ¼         31.1                 6 1/2         2.95

12 ¾         32.4                 7               3.17

13 ¼         33.7                 8               3.63

13 ¾         34.9                 9               4.08

14 ¼         36.2                10              4.54

14 ¾         37.5                11              4.99

15 ¼         38.7                12              5.44

15 ¾         40.0                13              5.90

16 ¼         41.3                15              6.8

16 ¾         42.7                17              7.71

17 ¼         43.8                19             8.62

17 ¾         45.1                21             9.52

18 ¼         46.4                23            10.43

18 ¾         47.6                25            11.34

19 ¼         48.9                27            12.24

19 ¾         50.2                29            13.15

20 ¼         51.4                31            14.06

20 ¾         52.7                33            14.97

21 ¼         53.9                35            15.87

21 ¾         55.3                37            16.78

22 ¼         56.5                39            17.69

22 ¾         57.8                42            19.05

23 ¼         59.1                45            20.41

23 ¾         60.3                48            21.77

24 ¼         61.6                51            23.13

24 ¾         62.9                54            24.49

25 ¼         64.1                57            25.85

25 ¾         65.4                60            27.21

26 ¼         66.7                63            28.57

26 ¾         67.9                66            29.93

27 ¼         69.2                69            31.29

27 ¾         70.5                72            32.65

28 ¼         71.7                75            34.01

28 ¾         73.0                78            35.37

29 ¼         74.3                81            36.73

29 ¾         75.6                84            38.10

30 ¼         76.8                87            39.46

30 ¾         78.0                90            40.82

31 ¼         79.4                93            42.18

31 ¾         80.7                97            44.0

32 ¼         81.9             101             45.8

32 ¾         83.2             105             47.62

33 ¼         84.5             110             49.89

33 ¾         85.7             115             52.15

34 ¼         87.0             120             54.42

34 ¾         88.3             125             56.69

35 ¼         89.5             130             58.96

35 ¾         90.8             135             61.22

36 ¼         92.1             140             63.49

36 ¾         93.4             145             65.76

37 ¼         94.6             150             68.08

37 ¾         95.9             155             70.29

38 ¼         97.2             160             72.56

38 ¾         98.4             165             74.83

39 ¼         99.7             170             77.10

39 ¾        101.0            175             79.37

40 ¼        102.2            180             81.63

40 ¾        103.5            185             83.90

41 ¼        104.8            190             86.17

41 ¾        106.1            195             88.44

42 ¼        107.3            200             90.7

42 ¾        108.6            205             92.9

43 ¼        109.8            210             95.3

43 ¾        111.1            215             97.5

44 ¼        112.4            220             99.8

44 ¾        113.7            225           102.1

45 ¼        114.9            230           104.3

45 ¾        116.2            235           106.6

46 ¼        117.5            240           108.8

46 ¾        118.7            245           111.1

47 ¼        120               250           113.4

47 ¾        121.2            255           115.6

48 ¼        122.5            260           117.9

48 ¾        123.8            265           120.2

49 ¼        125.1            270           122.5

49 ¾        126.4            275           124.7

50 ¼        127.6            280           127

50 ¾        128.9            285           129.3

51 ¼        130.2            290           131.5

51 ¾        131.4            295           133.8

52 ¼        132.7            300           136.1