Unfortunately, hv035 does not identify the eligibility of a specific child. I wish it did. Instead, it is the number of eligible children in the household and it is the same number for every record in the PR file (within the same household), regardless of age, etc. You can open the PR file and enter these lines:

keep if hvidx==1
tab hv035

You will see that there are 843 households with one eligible child, 653 with two, etc. The number of children will be 1*843 + 2*653 + ... = 2656. That, not 1654 or 2705, is the correct number of eligible children.

There is no need to do a merge. In the PR file the height-for-age variable is hc70. It is non-missing for 2636 children, although there are flagged and out-of-range values. The calculation of stunting would just use the hc70 values that are >-600 and <600. In the KR file the height-for-age variable is hw70. It is non-missing for 2214 children, including values that are flagged or out of range. Those 2214 children are the children in the household file whose mother is also in the household file and was interviewed. That is, if the mother has died or does not live in the same household as the child or was not interviewed, then the child who was in the PR file will not also be in the KR file.

DHS tables normally base the stunting (etc.) estimates on the children in the PR file, rather than the somewhat smaller number in the KR file. Children whose mother is not in the same household are generally a little worse off.

I suggest that you read about "_merge", a variable that is constructed whenever you do a merge. Normally you only want cases for which _merge===3, so you include a line "keep if _merge==3". Something else that I often do with complicated merges is to construct a variable that identifies the file. For example, after opening a PR file I will put "gen in_PR=1", and after opening a KR file I will have "gen in_KR=1". Then after the merge I could put "keep if in_PR==1 & in_KR==1", for example. If you do either of these things you should be able to discard the extra cases that are not in both files. I also do not use the new version of merge, with m:1, 1:m, etc., because it is too easy to get reversed and make a mistake.

The household selection for anthropometry across DHS surveys is quite standardized. In most of the cases, the households selected for anthropometry is a sub-sample consisting of one half or one third of the households selected for the women survey, depending on the sample size and fertility level. In a few countries with low fertility rate, or in some special cases for the purpose of a specific indicator related to children under five, anthropometry is conducted in all households selected for the women survey. In case of sub-sample selection of households for anthropometry, the selection procedure is systematic. In all cases, DHS never select children within household for anthropometry; it is always applied to all children under five found in the selected household. This is for survey efficiency considerations. All Uganda DHS surveys followed the standard procedure for anthropometry. Hope this is helpful.
Thanks