Before I try to match this myself, I want to suggest that you try to get a match using the PR file rather than the KR file. This is the most likely problem: all the children in the household are included in that table--not just the children whose mothers are in the household, i.e. the children in the KR file. Can you let me know whether that takes care of the problem?

Open the PR file for this survey (EGPR61FL.dta). Then enter "summarize hc70 if hc70<=600 & hv103==1 [iweight=hv005/1000000]". You will see that the weighted number of cases is 13601.1425, which rounds to 13601. Perhaps you were overlooking the footnote to table 12.4, which states that the table is restricted to children who slept in the household the night before. That is, you must restrict to hv103=1. Also ignore or drop the cases with hv70>600, because those measurements are out of range.