Less fat/more weight?

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I think I know the answer to this, but it is still bizarre to me. This is the third time this has happened.

I lose 20 pounds, 3 pounds from my target weight. But I look flabby - I can grab and handful of loose 'apron fat'. Suddenly - literally overnight - I gain 3 pounds. The day after that it starts to go away and within a week I'm back to where I was.

But the flab is gone. Stomach all tight (no perfect abs, but tight and not sagging).

I am not a big exerciser. But I take a really brisk (4 mph) 45 minute walk every evening plus at least another half hour walking throughout the day.

I am thinking that this - almost there/gain/solidify pattern is my body burning fat and building muscle. But is that possible with just walking? I can see it on my legs and bottom - which look great - but didnt' expect it on my arms and abs. I've cycled almost down to my target weight and up 3 pounds 3 times now. But inches keep coming off.