～気味: A little bit of this, a little bit of that

Introduction

I hope you enjoyed learning about っぽい, because this grammar's a bit similar... although it has its own flavor, for sure. And it tastes... a bit sweet? What a pleasant surprise!

～気味ぎみ: ... Your lunch money!

構成こうせい

• 

  Verb stemぎみ

• 

  Nounぎみ

  Example:
  → 風邪かぜ気味ぎみなので、今日きょうは休やすみます。
  ”I'm feeling a bit under the weather, so I'll take today off.”

In a nutshell, 気味ぎみ is a suffix that means "a bit". It tends to be used in negative contexts, and often attaches to words that refer to someone's physical/mental condition, like 風邪かぜ ("a cold"), 疲つかれ ("tired"), etc. But there are a couple of different ways we can use 気味ぎみ, so don't think you can get off easy!