Do I sense a bit of sarcasm in this question? Along with just a pinch of righteous indignation? I know this question is six years old, but I feel like answering anyway.

Of course Reagan increased military spending during his presidency. But I think conservative Republicans value a strong military (along with a simplification in the tax code), and that's probably what makes Reagan so popular with the party.

And despite what your question implies, being for smaller government doesn't necessarily mean you oppose ANY and EVERY type of increase in government size; you may support increasing the government in some aspects (like the defense budget), while oppose increasing the government in others (like taxes).