= Solution
For subject $i=1,\ldots,100$ and $t_j\in\{0,2,4,6,8,10\}$, the <random-intercept linear mixed model> is
$$
Y_{ij}=\beta_0+\beta_1t_j+b_i+\varepsilon_{ij},\qquad
b_i\overset{\mathrm{iid}}\sim N(0,\tau^2),\qquad
\varepsilon_{ij}\overset{\mathrm{iid}}\sim N(0,\sigma^2).
$$
All subject <random effects> and measurement errors are mutually independent. The <fixed effects> $\beta_0,\beta_1$ describe the population mean baseline and weekly gain. Conditional on $b_i$, a person's observations have independent <normal distributions>; after integrating out $b_i$, their <covariance> is $\tau^2$ at distinct weeks and their common <variance> is $\tau^2+\sigma^2$. Therefore their <correlation> is $\tau^2/(\tau^2+\sigma^2)$.
This <Gaussian linear mixed model> permits correlated repeated readings while keeping different subjects independent. The fitted <standard deviations> are $\widehat\tau=21.67593$ kg and $\widehat\sigma=14.23496$ kg, giving within-person <correlation> about $0.699$. All persons still have the same latent weekly slope in this model.
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