Regardless, this post is quite low-effort -- could you please at least add a bit more to your concept (at the very least, number of hands playing at this table and rough effective stack sizes, or at least what they vary between and frequency, e.g. "10-handed, two shortstacks with 40bb, five people around 100bb, two including straddle at 160bb, hero covers"). Also, you should offer what range you're opening here and why instead of just expecting the magic internet folks to bring the wizardry, and then you're likelier to get responses.
Seems okay, does JTs+ mean all suited broadways? I tend to fold QTs/KTs/KJs up front.
With BB calling I'm usually raising to around $20-25 depending on what the normal raise size looks like with most of the range I'm playing. I think I'd probably fold 77 up front in this spot too, since you're presumably basing the 50bb on $2? Like if there's a bunch of people sitting with $100 against a straddle to $4, I'm tightening up a little bit up front and continuing to be loose in late.
I keep my raising range about the same w/ or w/o the straddle. (This is assuming my stack is at least 100bb w/o considering straddle.) What can change it for me is how often the straddle defends.