I encountered 配慮 in my word list. Understanding how 慮 contributes to its meaning (which is "consideration") is not very difficult to grasp considering that 遠慮 occurs commonly in daily life. But when I try to associate 配 with 配る and 心配 (and adding 配慮 to the mix), I feel that this kanji does not seem to have a "unifying meaning" associated to it, unlike 木 (although, it might be an unfair comparison because it's a 象形文字). I understand that it's hopeless trying to unify meanings associated to certain kanjis like 占める and 占う. But what about 配？
配 is commonly encapsulated in English with "distribute", but you might also capture much of it with the word "allot", in the sense of allotting each its due. So 配慮 would give you "allotting-consideration", or more idiomatically, "paying consideration".
Source: Comparing all the kanji compounds for 配 in the スーパー大辞林.