Box P is 25% heavier than Box Q and Box R is 75% heavier than Box P. Express the weight of Box R as a percentage of the weight of Box Q.

1. Represent Box P in terms of Box Q after a 25% increase.

Let the weight of Box Q be $100$ units.

Since Box P is $25\%$ heavier than Box Q,
$P = 100\%+25\%=125\%\text{ of }Q$
$P=1.25\times 100=125\text{ units}.$

2. Represent Box R in terms of Box Q after a further 75% increase from Box P.

Since Box R is $75\%$ heavier than Box P,
$R=100\%+75\%=175\%\text{ of }P$
$R=1.75\times 125=218.75\text{ units}.$

Therefore, Box R is
$\frac{218.75}{100}\times 100\%=218.75\%$
of the weight of Box Q.