Well, sure, and the dying Giant Bug might fall on top of you in its death throes and squash you like a… well… bug.
I still saying blasting a big hole in a critter is going to be “effective”, but obviously the bigger the hole/greater the damage the quicker any impending demise will be.
If we assume they scale (magically) in speed like size and the spider means business, I’d guess I’m mortally wounded before my sword is drawn and probably before my hand even touches the grip. Blink and you miss it.
We’re defenseless against any ambush predator in their territory. Imagine a hungry bobbit worm that’s as big around as a manhole cover and it knows you’re there. Or an ant lion. Or a star nosed mole.
Handgun bullets maybe, but rifle bullets will go through quite heavy armor.
Level I armor will protect you against .22LR and not much else.
Level II will protect you from common handgun rounds like 9mm and .357.
Level III will protect you from lighter rifle rounds like the 5.56 intermediate cartridge of an AR-15, up to the 7.62 NATO cartridge.
Level IV will protect you from full power rifle cartridges like the .30-06.
(we’ll ignore sub-categories like Level IIA for this discussion)
I’m guessing scaled-up insect armor will be somewhere around Level II to Level III. An AR-15 will probably have some trouble getting through it, but it won’t stop a round from a decent hunting rifle or a heavy shotgun slug.
A .50 BMG like a Barret M82 is going to go right through that insect armor.
Law enforcement officers are typically going to be armed with handguns, which aren’t going to be effective. They will also have shotguns available but I don’t think they’ll have slugs for them. SWAT teams will have high-powered rifles which can do the trick. The National Guard will have plenty of weapons that can take out the big bugs.
AS the 1962 Topps presentation makes clear, Army weapons are effective against giant insects
This is the kind of practical, down-to-Earth advice I come to the Straight Dope for! This message board is a better place because of you. Thank you. 
Magic? Poppycock. This is normal, everyday radiation making them huge, of course. Perfectly natural.
This is FQ. Let’s do some envelope math!
The exterior shell of an ant, technically called the cuticle, has a wife range of thickness between species, from about 1 to 100 micrometers. For simplicity, let’s say 50 micrometers, or 0.005 centimeters.
There’s also a huge variety of overall size. Again for simplicity, let’s take the middle of the range for the common carpenter ant: 9mm.
Let’s say the ant is enlarged to 10 feet in length (because it’s very close to three meter and because it’s fun to annoy people by mixing unit types). That’s 3048 millimeters, or a little less than 350 times bigger than the original ant; we’ll use that, again, for simplicity.
If the cuticle is 0.005 centimeters thick, increasing it by 350 gets you a thickness of 1.75 centimeters.
We’d need a materials scientist for insight into the tensile strength of chitin at that thickness, but instinctively that feels like it would be less effective armor than I was speculating above.
So you’re right, a decent handgun should punch right through.
Edit to add: I wouldn’t have predicted this would be the topic to get my EO Wilson off the shelf, but I’m glad for the opportunity.
Do you want 30 inch diameter bobbit worms? Because this is how you get 30 inch diameter bobbit worms.
Giant Ant? I’d expect the authorities to use a giant magnifying glass. I see the same effect was generated by flamethrowers. Carry on.
How about a punt gun?
Spiders (and other bugs) often lose entire limbs to accidents or predators, which results in a pretty big hole. Yet they seem to survive just fine. (At least, I’ve seen plenty of spiders walking around with fewer than their full complement of legs.) Anatomically speaking, is there something more survivable about making a hole at a joint versus making a hole elsewhere in the exoskeleton?
Also, doesn’t diatomaceous earth kill arthropods by making lots of tiny cuts and holes in their exoskeleton? Again, this doesn’t cause the creature to immediately drop and bleed to death. Diatomaceous earth works as a pesticide precisely because it’s slow-acting enough to allow social insects time to pick it up on their legs and track it all over their burrows and nests, thus contaminating and killing a lot of their kin who never came in contact with the initial source. Why would holes caused by diatomaceous earth take hours or days to kill a small spider, but holes caused by bullets result in instantaneous immobilization in a giant spider?
I think that moves past the OP’s “handheld weapons” into technically man-portable weapons. I presumed from the OP that it’s something a more-or-less normal, or at least, physically fit human could fire from the hip or the shoulder as it was. Punt guns being fired from a small boat or prone position.
Personally, I’d skip to the end and get a backpack based industrial insecticide sprayer. Fuck handguns, let’s go straight to chemical warfare!
Note - only the OP’s title, not body of text, specified bullets thank you!
My thought was something the everyday person might carry before the National Guard or local law enforcement gets involved. I realize that’s a lot different today as opposed to when a movie like THEM! was released.
Take a look at his channel. You might re-define “every day carry”.
Speed mostly doesn’t scale with size. Neither does jumping distance, for that matter.
If we’re going to nitpick the scaling effects, then we should also ask whether every aspect of the critter is being perfectly scaled up 1-to-1 — which means it has the same number of cells, before and after, but now those cells are bizarrely huge — or if the number of cells is being multiplied to generate the size. Per the octupling rule for increasing volume when an object is enlarged in three dimensions, and per my envelope math above, a 9mm ant which grows to 10 feet will be 350 times longer but will have 2800 times the number of cells.
This is a consideration, perhaps, because now the critter’s brain and general neurological system will likely be a whole lot more complex, perhaps resulting in something like emergent intelligence and unexpectedly sophisticated behavior, unlike an ant that has simply been magically inflated.
Which means if you shoot at the ant, the ant might pull out a gun and shoot back. 
On the contrary. There is always the option of just dropping on you and squashing you with its weight, as Sam Gamgee could attest. You’re right about using the sword against it, though.
Spiders have an autotomy mechanism for dealing with leg injuries, specifically, that wouldn’t apply to body injury. Hell, some spiders detach their own pedipalps for sexual purposes.
Here’s a fairly dated but classic reference to how spider leg autotomy works:
https://journals.biologists.com/jcs/article/s3-98/43/331/64316/Spider-Leg-muscles-and-the-Autotomy-Mechanism
Most favored among insects is of course the bee-bee gun.
