I think LizardGirl is pointing you in the best direction, more data oriented than observation oriented.
I have had him for over a week now and he has doubled in size
It's hard to know what this means, or to discuss.
I feed him 4oz. a night and he eats all of it
If he's eating everything, then he may not be getting enough, despite the growth? Most people free-feed.
You mention a high level of running. That was a huge problem with Sophie, who ran, ran, and ran - but wouldn't eat enough quantity. We had to make some diet changes to stop a couple of weight drops and really ramp up fat and protein percentages. As she gets down close to 300 grams, she starts feeling a bit bony. We've pretty much got her at a balance now.
Here is some data. Start from the bottom. You will see explosive growth while still a baby; 25% weight gain her first week here. Then the growth tapers off a bit. Then some yo-yo periods that caused me a lot of grief - losing, regaining, losing, regaining, and finally coming to a steady balance. At 66 weeks, she weighs exactly the same as she did at 13 weeks - supposedly not even full grown - but seems to be in fine shape. (It's easier to follow this in my docs because I color-code the data, which makes it easier to see.
......................................................
weigh-ins (Monday afternoons) Percentage gain / loss rounded to nearest .1% (usually))
66 weeks: 318 grams (11.22 ounces) (+4) (+0.65%)
65 weeks: 314 grams (11.08 ounces) (-4) (-1.25%)
64 weeks: 318 grams (11.22 ounces) (-4) (-1.25%)
63 weeks: 322 grams (11.36 ounces) (+2) (+0.6%)
62 weeks: 320 grams (11.29 ounces) (+0) (+0.0%)
61 weeks: 320 grams (11.29 ounces) (+0) (+0.0%)
60 weeks: 320 grams (11.29 ounces) (+6) (+1.9%)
59 weeks: 314 grams (11.08 ounces) (+2) (+0.65%)
58 weeks: 312 grams (11.01 ounces) (+6) (+1.95%)
57 weeks: 306 grams (10.79 ounces) (+0) (+0.00%)
56 weeks: 306 grams (10.79 ounces) (+2) (+0.65%)
55 weeks: 304 grams (10.72 ounces) (-2) (-0.65%)
54 weeks: 306 grams (10.79 ounces) (+4) (+1.3%)
53 weeks: 302 grams (10.65 ounces) (+2) (+0.7%)
52 weeks: 300 grams (10.58 ounces) (+4) (+1.35%)
*****(One year old.)*****
51 weeks: 296 grams (10.44 ounces) (+8) (+2.8%)
50 weeks: 288 grams (10.16 ounces) (-6) (-2.0%)
49 weeks: 294 grams (10.37 ounces) (+0) (+0.0%)
48 weeks: 294 grams (10.37 ounces) (+2) (+0.7%)
47 weeks: 292 grams (10.30 ounces) (+6) (+2.1%)
46 weeks: 286 grams (10.09 ounces) (+2) (+0.7%)
45 weeks: 284 grams (10.02 ounces) (-2) (+0.7%)
****(Total loss from 336 gram level: 52 grams. -15.5%)
44 weeks: 286 grams (10.09 ounces) (-14) (-4.7%)
43 weeks: 300 grams (10.58 ounces) (-8) (-2.6%)
42 weeks: 308 grams (10.86 ounces) (+2) (+0.65%)
41 weeks: 306 grams (10.79 ounces) (+0) (+0.0%)
40 weeks: 306 grams (10.79 ounces) (-12) (-3.8%)
****(Total loss from 336 gram level: 30 grams. -8.9%)
39 weeks: 318 grams (11.22 ounces) (+0) (+0.0%)
38 weeks: 318 grams (11.22 ounces) (+8) (+2.6%)
37 weeks: 310 grams (10.94 ounces) (-6) (-1.9%)
****(Total loss from 336 gram level: 26 grams. -7.7%)
36 weeks: 316 grams (11.15 ounces) (+0) (+0.0%)
35 weeks: 316 grams (11.15 ounces) (+4) (+1.3%)
34 weeks: 312 grams (11.01 ounces) (-6) (-1.9%)
33 weeks: 318 grams (11.22 ounces) (-10) (-3.2%)
32 weeks: 328 grams (11.57 ounces) (-8) (-2.4%)
31 weeks: 336 grams (11.85 ounces) (+2) (+0.6%)
30 weeks: 334 grams (11.78 ounces) (+4) (+1.2%)
29 weeks: 330 grams (11.64 ounces) (-4) (-1.2%)
28 weeks: 334 grams (11.78 ounces) (+2) (+0.6%)
27 weeks: 332 grams (11.71 ounces) (+4) (+1.2%)
26 weeks: 328 grams (11.57 ounces) (+4) (+1.2%)
25 weeks: 324 grams (11.43 ounces) (+6) (+1.9%)
24 weeks: 318 grams (11.22 ounces) (+14) (+4.6%)
23 weeks: 304 grams (10.72 ounces) (+14) (+4.8%)
22 weeks: 290 grams (10.23 ounces) (+0) (+0.0%)
21 weeks: 290 grams (10.23 ounces) (-18) (-5.9%)
*****(Total loss from 330 gram level: 40 grams. -12.3%)
20 weeks: 308 grams (10.86 ounces) (-4) (-1.3%)
19 weeks: 312 grams (11.01 ounces) (-10) (-3.1%)
18 weeks: 322 grams (11.36 ounces) (+6) (+1.9%)
17 weeks: 316 grams (11.15 ounces) (-4) (-1.3%)
16 weeks: 320 grams (11.29 ounces) (-10) (-3.0%)
15 weeks: 330 grams (11.64 ounces) (+4) (+1.2%)
14 weeks: 326 grams (11.50 ounces) (+8) (+2.5%)
13 weeks: 318 grams (11.22 ounces) (+4) (+1.3%)
12 weeks: 314 grams (11.08 ounces) (+12) (+4%)
11 weeks: 302 grams (10.65 ounces) (+26) +(9.4%)
10 weeks: 276 grams (9.74 ounces) (+34) (+14%)
9 weeks: 242 grams (8.54 ounces) (+22) (+10%)
8 weeks: 220 grams (7.76 ounces) (+38) (+20.9%)
7 weeks: 182 grams (6.42 ounces) (+36) (+24.7%)
6 weeks: 146 grams (5.15 ounces)