The short answer is: very little weight.
Maybe unless done by an astrologer with actual understanding of the twin flame journey (and I don’t just mean using it as a buzzword, I mean they know the journey.
Sun sign compatibility is like the smallest piece of the puzzle. Twin flame astrology actually looks for tension and challenging aspects because those create the growth you need. Soulmates get harmonious charts - twin flames get complicated ones that force both people to evolve.
What you’re describing with “hits every other sign” is exactly right. The real indicators are things like kundalini awakening (that intense energy rising through your body when you’re together), telepathic connection, seeing them in dreams, feeling like you’ve known them forever, and those constant number synchronicities. Astrologers who work with twin flames say the charts often look difficult on purpose - one even noted twin flames are frequently one, three, five, or six signs apart, which creates uncomfortable aspects.
For Aries-Cancer specifically, you’re working with divine masculine and divine feminine energies. Aries brings courage and helps Cancer step out of the shell. Cancer provides the emotional depth and security that grounds Aries. Yes, you’ll clash over vulnerability, pacing, and communication. Fire doesn’t want to feel things deeply while water lives there. But those clashes teach both of you what you’re avoiding.
Look at your full charts if you want - moon signs, Venus, Mars, rising signs, North Node connections. You might find more compatibility than you think. But even if you don’t, it doesn’t matter. Twin flames work when both people do the inner work.