PROPWT builds from original national statistical office weights which address sample and non-response bias, and adds CTUR adjustments that remove bad diary cases and balance the distribution of days of the week for men and women of different age groups in employment and not in employment. PROPWT does not balance the number of diaries from each country relative to the others or balance the number of diaries collected in different surveys from the same country.
In some cases (depending on which surveys you compare), the diary sample size varies considerably. To prevent a large survey from overwhelming smaller surveys, you might consider a number of strategies.
One way is to run your model separately on each country (or survey). Another way is to create your own weight that adjusts the size of the larger surveys to the smaller surveys. We recommend that you adjust the larger surveys to be of a similar size relative to the smaller surveys so that any unusual individuals or diary days in the smaller survey do not have a disproportionate effect.
Something you should keep in mind is that the American Time Use Survey (ATUS, survey=2003) collects different sized samples every year from 2003-2015 - all of which are in the MTUS. Much has happened in the USA over the 10 years from 2003 to 2015, and for that country and survey you have within country cross-time change, as well as an enormous number of diaries. You might consider limiting the ATUS (USA 2003) data to a more limited number of years rather than taking the whole of the ATUS.