Dave Cushman wrote:
>I do not know which came first but I suspect the verb did


According to OED, the verb came first

Eke, verb
To increase, add to, lengthen.

c1200 The holie man fasted for to eken his holinesse.
1599 As they say, Every thing Eiketh.
1755  Without eking or curtailing God's precious truth.
1829  The moaning brook, that ekes its weary speed.

Eke, noun
A short straw or wooden cylinder on which a beehive is placed to
increase its capacity.

1857 Underlay. Now called ekes; additional bands of straw placed
beneath the hive.

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