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Get column rank from values in selected row
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The reason for your problem is that you are using column names as data.

Your centiles need to go into a separate table.

CREATE TABLE centiles (ID INTEGER PRIMARY KEY, cent TEXT);
CREATE TABLE weights  (ID INTEGER PRIMARY KEY, age INTEGER, WEIGHT INTEGER, CENT_ID INTEGER REFERENCES centiles(ID), UNIQUE(age,weight));

SELECT c.cent FROM weights w JOIN centiles c ON (c.ID = w.cent_id) WHERE w.age = 3 and w.weight = 9;