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I need the correct verb form in present tense for the phrase "...the cost and size of... decrease". When I google "as the cost and size of" or smth like that, both forms in present can be found: plural and singular.
For example,

As the cost and size of devices falls<br>

As the cost and size of the sensors continue to...

I hope that the use of plural is more correct in this case, but I see also that the common definite article may influence it.
It is for a scientific paper which is written in English (US) addressed globally.

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I doubt in casual use any native speaker would think twice, regardless of which you used. However when considering the grammar itself then the plural is correct, especially when discussing essentially disparate things.

You might also hear the word "both" added to better highlight that there are two things which have changed:

Both the cost and size of devices fall as they evolve.

The cost and size of devices both fall as they evolve.

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